Type:	Package
Title:	Parametric Mortality Models, Life Tables and HMD
Version:	2.2.0
Maintainer:	Marius D. Pascariu <mpascariu@outlook.com>
Description:	Fit the most popular human mortality 'laws', and construct full and abridge life tables given various input indices. A mortality law is a parametric function that describes the dying-out process of individuals in a population during a significant portion of their life spans. For a comprehensive review of the most important mortality laws see Tabeau (2001) <doi:10.1007/0-306-47562-6_1>. Practical functions for downloading data from various human mortality databases are provided as well.
License:	MIT + file LICENSE
LazyData:	TRUE
Depends:	R (≥ 3.0.0)
Imports:	RCurl (≥ 1.95), pbapply (≥ 1.3-4), tidyr (≥ 0.8.1), rvest (≥ 1.0.3), httr (≥ 1.4.5), methods
Suggests:	testthat, knitr, rmarkdown
URL:	https://github.com/mpascariu/MortalityLaws
BugReports:	https://github.com/mpascariu/MortalityLaws/issues
Encoding:	UTF-8
RoxygenNote:	7.3.3
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2026-05-05 06:43:17 UTC; masax
Author:	Marius D. Pascariu [aut, cre, cph], Vladimir Canudas-Romo [ctb]
Repository:	CRAN
Date/Publication:	2026-05-05 07:10:08 UTC

MortalityLaws: Parametric Mortality Models, Life Tables and HMD

Description

Fit the most popular human mortality 'laws', and construct full and abridge life tables given various input indices. A mortality law is a parametric function that describes the dying-out process of individuals in a population during a significant portion of their life spans. For a comprehensive review of the most important mortality laws see Tabeau (2001) doi:10.1007/0-306-47562-6_1. Practical functions for downloading data from various human mortality databases are provided as well.

Details

To learn more about the package, start with the vignettes: browseVignettes(package = "MortalityLaws")

Author(s)

Maintainer: Marius D. Pascariu mpascariu@outlook.com (ORCID) [copyright holder]

Other contributors:

• Vladimir Canudas-Romo [contributor]

See Also

Useful links:

• https://github.com/mpascariu/MortalityLaws

• Report bugs at https://github.com/mpascariu/MortalityLaws/issues

AHMD sample Data object generated by the ReadAHMD() function.

Description

AHMD sample Data object generated by the ReadAHMD() function.

Usage

AHMD_sample

Format

An object of class ReadAHMD of length 5.

Value

A sample of demographic data in a data.frame

AIC function for MortalityLaw

Description

AIC function for MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
AIC(object, ...)

Arguments

Value

model AIC value

region codes

Description

region codes

Usage

AUSregions()

Value

a vector

Country codes

Description

Country codes

Usage

CANregions()

Value

a vector

CHMD sample Data object generated by the ReadCHMD() function.

Description

CHMD sample Data object generated by the ReadCHMD() function.

Usage

CHMD_sample

Format

An object of class ReadCHMD of length 5.

Value

A sample of demographic data in a data.frame

HMD sample Data object generated by the ReadHMD() function.

Description

HMD sample Data object generated by the ReadHMD() function.

Usage

HMD_sample

Format

An object of class ReadHMD of length 5.

Value

A sample of demographic data in a data.frame

Country codes

Description

Country codes

Usage

HMDcountries()

Value

a vector

HMD Indices

Description

HMD Indices

Usage

HMDindices()

Value

a vector

Heligman-Pollard Mortality Law - 8 parameters - 1980

Description

Heligman-Pollard Mortality Law - 8 parameters - 1980

Usage

HP(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

HP(x = 0:100)

Heligman-Pollard 2 Mortality Law - 8 parameters

Description

Heligman-Pollard 2 Mortality Law - 8 parameters

Usage

HP2(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

HP2(x = 0:100)

Heligman-Pollard 3 Mortality Law - 9 parameters

Description

Heligman-Pollard 3 Mortality Law - 9 parameters

Usage

HP3(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

HP3(x = 0:100)

Heligman-Pollard 4 Mortality Law - 9 parameters

Description

Heligman-Pollard 4 Mortality Law - 9 parameters

Usage

HP4(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

HP4(x = 0:100)

JMD sample Data object generated by the ReadJMD() function.

Description

JMD sample Data object generated by the ReadJMD() function.

Usage

JMD_sample

Format

An object of class ReadJMD of length 5.

Value

A sample of demographic data in a data.frame

region codes

Description

region codes

Usage

JPNregions()

Value

the vector

Compute Life Tables from Parameters of a Mortality Law

Description

Generate a complete life table directly from the fitted parameters of a parametric mortality model. This function evaluates the mortality law at the given ages and passes the resulting death rates (mx) or death probabilities (qx) to LifeTable for further computation of all standard life-table columns (lx, dx, Lx, Tx, ex, etc.).

Usage

LawTable(x, par, law, sex = NULL, lx0 = 1e+05, ax = NULL)

Arguments

Details

This function is designed to work with models that have been fitted externally (e.g., via MortalityLaw or by hand). The par argument must contain the estimated coefficients of the mortality law, and law must be one of the valid codes listed by availableLaws.

Important caveat: age scaling during fitting

Several mortality laws (e.g., Gompertz, Makeham) internally scale the age vector during optimisation to ensure numerical stability. If the model was fitted using MortalityLaw over an age range [a, b], the published coefficients correspond to the scaled ages, not the original ages. Consequently, LawTable will only produce valid life tables for ages \ge a (the lower bound of the fitting range). Attempting to use the same coefficients at younger ages will yield incorrect results (e.g., life expectancy at age 25 will equal that at age 45).

To determine which models apply age scaling, run:

A <- availableLaws()$table
A[, c("CODE", "SCALE_X")]

Models with SCALE_X = TRUE rescale the age vector internally. When using LawTable with such a model, make sure the x argument starts from the same lower age bound used during fitting.

For models that do not scale (e.g., Heligman-Pollard "HP"), this limitation does not apply, and LawTable can be used for any age range.

Value

An object of class "LifeTable" containing the following components:

Author(s)

Marius D. Pascariu

See Also

LifeTable for constructing life tables from raw mortality data; MortalityLaw for fitting parametric mortality models; availableLaws for the list of implemented laws and their scaling behaviour.

Examples

# Example 1 --- Makeham --- multiple life tables from a matrix of parameters

x1 <- 45:100
L1 <- "makeham"
C1 <- matrix(
  c(0.00717, 0.07789, 0.00363,
    0.01018, 0.07229, 0.00001,
    0.00298, 0.09585, 0.00002,
    0.00067, 0.11572, 0.00078),
  nrow = 4,
  dimnames = list(1:4, c("A", "B", "C"))
)

LawTable(x = x1, par = C1, law = L1)

# ---- Important note on age scaling ----

# The Makeham model applies internal age scaling during fitting.
# If the coefficients above were estimated over ages 45-100, the life
# table produced by LawTable is valid only from age 45 onward.

# ---- Example 1B: correct usage ----
LawTable(x = 45:100, par = c(0.00717, 0.07789, 0.00363), law = L1)

# ---- Example 1C: incorrect usage ----
# The code below uses the same coefficients but starts at age 25.
# Because the model was fitted on scaled ages (starting at 45),
# the life table at age 25 will be meaningless (e.g., e25 equals e45).
## Not run: 
LawTable(x = 25:100, par = c(0.00717, 0.07789, 0.00363), law = L1)

## End(Not run)

# ---- How to check which laws apply scaling ----
A <- availableLaws()$table
A[, c("CODE", "SCALE_X")]

# Example 2 --- Heligman-Pollard (no scaling) ---

x2 <- 0:110
L2 <- "HP"
C2 <- c(0.00223, 0.01461, 0.12292, 0.00091,
        2.75201, 29.01877, 0.00002, 1.11411)

LawTable(x = x2, par = C2, law = L2)

# Because "HP" does NOT scale the age vector, the output is valid for
# any starting age. Compare:
LawTable(x = 3:110, par = C2, law = L2)
# Note that e3 = 70.31 in both tables, confirming consistency.

Compute Life Tables from Mortality Data

Description

Construct either a full (single-year age intervals) or an abridged (wider age intervals) life table from a variety of input data types. The function accepts:

• Death counts and mid-interval population estimates (Dx, Ex)

• Age-specific death rates (mx)

• Death probabilities (qx)

• Survivorship curve (lx)

• Distribution of deaths (dx)

Only one of these input options needs to be provided; the others are ignored if present. The input can be a numeric vector, matrix, or data.frame. When a matrix or data.frame with multiple columns is supplied, the function computes one life table per column.

Usage

LifeTable(x, Dx = NULL, Ex = NULL,
             mx = NULL,
             qx = NULL,
             lx = NULL,
             dx = NULL,
             sex = NULL,
             lx0 = 1e5,
             ax  = NULL)

Arguments

Details

A life table (also called a mortality table or actuarial table) summarises the mortality experience of a population. For each age (or age interval) it reports:

• Death rates (mx) and death probabilities (qx)

• Survivorship (lx)

• Distribution of deaths (dx)

• Person-years lived (Lx) and total person-years remaining (Tx)

• Life expectancy (ex)

The life table is constructed sequentially: from the input data the function derives mx, then qx, then lx, dx, Lx, Tx, and finally ex. The constant-force-of-mortality (CFM) assumption is used to convert between mx and qx. If the sex argument is supplied, the first two values of the ax column are adjusted using the Coale-Demeny method, which accounts for the different infant mortality patterns between males and females.

Value

An object of class "LifeTable" containing the following components:

Author(s)

Marius D. Pascariu

See Also

LawTable for generating life tables from a fitted parametric mortality law; convertFx for converting between mortality measures.

Examples

# Example 1 --- Full life tables with different inputs ------------

y  <- 1900
x  <- as.numeric(rownames(ahmd$mx))
Dx <- ahmd$Dx[, paste(y)]
Ex <- ahmd$Ex[, paste(y)]

LT1 <- LifeTable(x, Dx = Dx, Ex = Ex)
LT2 <- LifeTable(x, mx = LT1$lt$mx)
LT3 <- LifeTable(x, qx = LT1$lt$qx)
LT4 <- LifeTable(x, lx = LT1$lt$lx)
LT5 <- LifeTable(x, dx = LT1$lt$dx)

LT1
LT5
ls(LT5)

# Example 2 --- Compute multiple life tables at once ------------

LTs <- LifeTable(x, mx = ahmd$mx)
LTs
# A warning is printed if the input contains missing values.
# Some of the missing values can be handled automatically.

# Example 3 --- Abridged life table -----------------------------

x  <- c(0, 1, seq(5, 110, by = 5))
mx <- c(.053, .005, .001, .0012, .0018, .002, .003, .004,
        .004, .005, .006, .0093, .0129, .019, .031, .049,
        .084, .129, .180, .2354, .3085, .390, .478, .551)
LT6 <- LifeTable(x, mx = mx, sex = "female")
LT6

# Example 4 --- Abridged life table using a custom 'ax' --------
# This example reuses the ages (x) and death rates (mx) from Example 3.
# Note that 'ax' must have the same length as 'x', otherwise an error
# will be returned.

my_ax <- c(0.1, 1.5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
           2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1)

LT7 <- LifeTable(x = x, mx = mx, ax = my_ax)

Check LifeTable input

Description

Check LifeTable input

Usage

LifeTable.check(input)

Arguments

Value

A list of life table validated data

LifeTable.core

Description

LifeTable.core

Usage

LifeTable.core(x, Dx, Ex, mx, qx, lx, dx, sex, lx0, ax)

Arguments

Value

A data.frame containing life table results

Fit Mortality Laws

Description

Fit parametric mortality models given a set of input data. The data can be supplied as death counts and mid-interval population estimates (Dx, Ex), age-specific death rates (mx), or death probabilities (qx). Use the law argument to specify the model to be fitted. Over 30 parametric models are currently implemented; run availableLaws to see the full list. Models can be fitted using maximum likelihood or by optimising a loss function. See the availableLF function for the implemented options.

Usage

MortalityLaw(x, Dx = NULL, Ex = NULL, mx = NULL, qx = NULL,
                law = NULL,
                opt.method = "LF2",
                parS = NULL,
                fit.this.x = x,
                custom.law = NULL,
                show = FALSE, ...)

Arguments

Details

Optimisation: The PORT routines (via nlminb) are used for unconstrained and box-constrained optimisation. Parameters are estimated on the log scale to ensure positivity, and the routine is set to allow up to 5000 iterations. When the optimisation method is "poissonL" or "binomialL", the AIC, BIC and log-likelihood are computed from the likelihood. Otherwise these are set to NaN.

Scaling of the age vector: For models that cover only a portion of the lifespan (e.g., adult or old-age mortality), the age vector x is automatically re-scaled as x = x - min(x) + 1 before fitting. This transformation improves numerical stability and helps the optimisation algorithm converge, especially when the starting age is far from zero. Models that apply this scaling are flagged with SCALE_X = TRUE in the table returned by availableLaws. When using predict.MortalityLaw or LawTable with such models, the same scaling is applied internally, so predictions remain consistent with the fitted coefficients.

Handling matrix input: If Dx, Ex, mx or qx are provided as matrices (with one column per population or time period), the function iterates over the columns and fits a separate model to each, returning a collection of results.

Value

An object of class "MortalityLaw", which is a list with the following components:

Author(s)

Marius D. Pascariu

See Also

availableLaws for a list of all implemented models; availableLF for loss function details; LifeTable for life table construction; ReadHMD for downloading data from the Human Mortality Database.

Examples

# Example 1: Fitting the Makeham model --------------------------
x  <- 45:75
Dx <- ahmd$Dx[paste(x), "1950"]
Ex <- ahmd$Ex[paste(x), "1950"]

M1 <- MortalityLaw(x = x, Dx = Dx, Ex = Ex, law = 'makeham')

M1
ls(M1)
coef(M1)
summary(M1)
fitted(M1)
predict(M1, x = 45:95)
plot(M1)


# Example 2: --------------------------
# We can fit the same model using a different data format
# and a different optimization method.
x  <- 45:75
mx <- ahmd$mx[paste(x), ]
M2 <- MortalityLaw(x = x, mx = mx, law = 'makeham', opt.method = 'LF1')
M2
fitted(M2)
predict(M2, x = 55:90)

# Example 3: --------------------------
# Now let's fit a mortality law that is not defined
# in the package, say a reparameterized Gompertz in
# terms of modal age at death
# hx = b*exp(b*(x-m)) (here b and m are the parameters to be estimated)

# A function with 'x' and 'par' as input has to be defined, which returns
# at least an object called 'hx' (hazard rate).
my_gompertz <- function(x, par = c(b = 0.13, M = 45)){
  hx  <- with(as.list(par), b*exp(b*(x - M)) )
  return(as.list(environment()))
}

M3 <- MortalityLaw(x = x, Dx = Dx, Ex = Ex, custom.law = my_gompertz)
summary(M3)
# predict M3 for different ages
predict(M3, x = 85:130)


# Example 4: --------------------------
# Fit Heligman-Pollard model for a single
# year in the dataset between age 0 and 100 and build a life table.

x  <- 0:100
mx <- ahmd$mx[paste(x), "1950"] # select data
M4 <- MortalityLaw(x = x, mx = mx, law = 'HP', opt.method = 'LF2')
M4
plot(M4)

LifeTable(x = x, qx = fitted(M4))

Download the Australian Human Mortality Database (AHMD)

Description

Download detailed mortality and population data for different provinces and territories in Australia, in a single object from the Australian Human Mortality Database.

Usage

ReadAHMD(what, regions = NULL, interval = "1x1", save = FALSE, show = TRUE)

Arguments

Details

(Description taken from the AHMD website).

The Australian Human Mortality Database (AHMD) was created to provide detailed Australian mortality and population data to researchers, students, journalists, policy analysts, and others interested in the history of human longevity. The project is an achievement of the Mortality, Ageing & Health research team in the ANU School of Demography under the supervision of Associate Professor Vladimir Canudas-Romo, in collaboration with demographers at the Max Plank Institute for Demographic Research (Rostock, Germany) and the Department of Demography, University of California at Berkeley.

The AHMD is a "satellite" of the Human Mortality Database (HMD), an international database which currently holds detailed data for multiple countries or regions. Consequently, the AHMD's underlying methodology corresponds to the one used for the HMD.

The AHMD gathers all required data (deaths counts, births counts, population size, exposure-to-risk, death rates) to compute life tables for Australia, its states and its territories. One of the great advantages of the database is to include data that is validated and corrected, when required, and rendered comparable, if possible, for the period ranging from 1971 thru 2016. For comparison purposes, various life tables published by governmental organizations are also available for download in PDF format.

Value

A ReadAHMD object that contains:

Author(s)

Marius D. Pascariu

See Also

ReadHMD ReadCHMD

Examples

# Download demographic data for Australian Capital Territory and
# Tasmania regions in 5x1 format

# Death counts. We don't want to export data outside R.
AHMD_Dx <- ReadAHMD(what = "Dx",
                    regions = c('ACT', 'TAS'),
                    interval  = "5x1",
                    save = FALSE)
AHMD_Dx

# Download life tables for female population in all the states and export data.
LTF <- ReadAHMD(what = "LT_f", interval  = "5x1", save = FALSE)
LTF

Download the Canadian Human Mortality Database (CHMD)

Description

Download detailed mortality and population data for different provinces and territories in Canada, in a single object from the Canadian Human Mortality Database.

Usage

ReadCHMD(what, regions = NULL, interval = "1x1", save = FALSE, show = TRUE)

Arguments

Details

(Description taken from the CHMD website).

The Canadian Human Mortality Database (CHMD) was created to provide detailed Canadian mortality and population data to researchers, students, journalists, policy analysts, and others interested in the history of human longevity. The project is an achievement of the Mortality and Longevity research team at the Department of Demography, Universite de Montreal, under the supervision of Professor Robert Bourbeau, in collaboration with demographers at the Max Plank Institute for Demographic Research (Rostock, Germany) and the Department of Demography, University of California at Berkeley. Nadine Ouellette, researcher at the Institut national d'etudes demographiques in Paris and member of the Mortality and Longevity research team at the Universite de Montreal, is in charge of computing all CHMD life tables and updating the CHMD web site.

The CHMD is a "satellite" of the Human Mortality Database (HMD), an international database which currently holds detailed data for multiple countries or regions. Consequently, the CHMD's underlying methodology corresponds to the one used for the HMD.

The CHMD gathers all required data (deaths counts, births counts, population size, exposure-to-risk, death rates) to compute life tables for Canada, its provinces and its territories. One of the great advantages of the database is to include data that is validated and corrected, when required, and rendered comparable, if possible, for the period ranging from 1921 thru 2011. For comparison purposes, various life tables published by governmental organizations are also available for download in PDF format.

Value

A ReadCHMD object that contains:

Author(s)

Marius D. Pascariu

See Also

ReadHMD ReadAHMD

Examples

# Download demographic data for Quebec and Saskatchewan regions in 1x1 format

# Death counts. We don't want to export data outside R.
CHMD_Dx <- ReadCHMD(what = "Dx",
                    regions = c('QUE', 'SAS'),
                    interval  = "1x1",
                    save = FALSE)

# Download life tables for female population. To export data use save = TRUE.
LTF <- ReadCHMD(what = "LT_f",
                regions = c('QUE', 'SAS'),
                interval  = "1x1",
                save = FALSE)

Download The Human Mortality Database (HMD)

Description

Download detailed mortality and population data for different countries and regions in a single object from the Human Mortality Database.

Usage

ReadHMD(
  what,
  countries = NULL,
  interval = "1x1",
  username,
  password,
  save = FALSE,
  show = TRUE
)

Arguments

Details

The Human Mortality Database (HMD) was created to provide detailed mortality and population data to researchers, students, journalists, policy analysts, and others interested in the history of human longevity. The project began as an outgrowth of earlier projects in the Department of Demography at the University of California, Berkeley, USA, and at the Max Planck Institute for Demographic Research in Rostock, Germany (see history). It is the work of two teams of researchers in the USA and Germany (see research teams), with the help of financial backers and scientific collaborators from around the world (see acknowledgements). The Center on the Economics and Development of Aging (CEDA) French Institute for Demographic Studies (INED) has also supported the further development of the database in recent years.

Value

A ReadHMD object that contains:

Author(s)

Marius D. Pascariu

Examples

## Not run: 


# Download demographic data for 3 countries in 1x1 format
age_int  <- 1  # age interval: 1,5
year_int <- 1  # year interval: 1,5,10
interval <- paste0(age_int, "x", year_int)  # --> 1x1
# And the 3 countries: Sweden Denmark and USA. We have to use the HMD codes
cntr  <- c('SWE', 'DNK', 'USA')

# Download death counts. We don't want to export data outside R.
HMD_Dx <- ReadHMD(what = "Dx",
                  countries = cntr,
                  interval  = interval,
                  username  = "user@email.com",
                  password  = "password",
                  save = FALSE)
HMD_Dx

# Download life tables for female population and export data.
LTF <- ReadHMD(what = "LT_f",
               countries = cntr,
               interval  = interval,
               username  = "user@email.com",
               password  = "password",
               save = TRUE)
LTF

## End(Not run)

Function to Download Data for a one Country

Description

Function to Download Data for a one Country

Usage

ReadHMD.core(what, country, interval, username, password, link)

Arguments

Value

A data.frame containing demographic data

Download the Japanese Mortality Database (JMD)

Description

Download detailed mortality and population data of the 47 prefectures in Japan, in a single object. The source of data is the Japanese Mortality Database.

Usage

ReadJMD(what, regions = NULL, interval = "1x1", save = FALSE, show = TRUE)

Arguments

Details

(Description taken from the JMD website).

The Japanese Mortality Database is a comprehensively-reorganized mortality database that is optimized for mortality research and consistent with the Human Mortality Database. This database is provided as a part of the research project "Demographic research on the causes and the socio-economic consequence of longetivity extension in Japan" (2011-2013), "Demographic research on longevity extension, population aging, and their effects on the social security and socio-economic structures in Japan" (2014-2016), and "Comprehensive research from a demographic viewpoint on the longevity revolution" (2017-2019) at the National Institute of Population and Social Security Research.

The Japanese Mortality Database is designed to provide the life tables to all the people who are interested in Japanese mortality including domestic and foreign mortality researchers for the purpose of mortality research. Especially because we have structured it to conform with the HMD, our database is suitable for international comparison, we put emphasis on the compatibility with the HMD more than our country's particular characteristics. Therefore, the life tables by JMD do not necessarily exhibit the same values as ones by the official life tables prepared and released by the Statistics and Information Department, Minister's Secretariat, Ministry of Health, Labor and Welfare according to the different base population or the methods for estimating the tables. When doing things other than mortality research, if life table that statistically displays our country's mortality situation is necessary, please use the official life table that has been prepared by the Statistics and Information Department, Minister's Secretariat, Ministry of Health, Labor and Welfare.

At the present time, we offer the data for All Japan and by prefecture. The project team is studying the methodology for estimating life tables along with data preparation. Therefore, the data may be updated when a new methodology is adopted. Please refer to "Methods" for further information.

Value

A ReadJMD object that contains:

Author(s)

Marius D. Pascariu

See Also

ReadHMD ReadCHMD

Examples

# Download demographic data for Fukushima and Tokyo regions in 1x1 format

# Death counts. We don't want to export data outside R.
JMD_Dx <- ReadJMD(what = "Dx",
                  regions = c('Fukushima', 'Tokyo'),
                  interval  = "1x1",
                  save = FALSE)
JMD_Dx

# Download life tables for female population in all the states and export data.
LTF <- ReadJMD(what = "LT_f", interval  = "5x5", save = FALSE)
LTF

Retrieve model-specific details for fitting

Description

Based on the chosen mortality law (or a custom law), this function retrieves the default starting parameters, the model information table, and whether the age vector should be scaled before fitting.

Usage

addDetails(law, custom.law = NULL, parS = NULL)

Arguments

Value

A list with components:

What age(s) are we looking at?

Description

What age(s) are we looking at?

Usage

ageMsg(what, x)

Arguments

Value

A scalar or character indicating age groups

MortalityLaws Test Data

Description

Dataset containing altered death rates (mx), death counts (Dx) and exposures (Ex) for the female population living in England & Wales in four different years: 1850, 1900, 1950 and 2010. This dataset is provided for testing purposes only. Download the actual data free of charge from https://www.mortality.org. Once a username and a password are created on the website, the function ReadHMD can be used for downloading.

Usage

ahmd

Format

An object of class list of length 3.

Source

Human Mortality Database

See Also

ReadHMD

Examples

head(ahmd$mx)

Check Data Availability in HMD

Description

Returns information about the data available in the Human Mortality Database (HMD), including the range of years covered by the life tables for each country or region.

Usage

availableHMD(link = "https://www.mortality.org/Data/DataAvailability")

Arguments

Value

A tibble.

Author(s)

Marius D. Pascariu

See Also

ReadHMD

Examples

availableHMD()

Check Available Loss Functions

Description

Returns information about the loss functions implemented for use with the optimisation procedure in the MortalityLaw function.

Usage

availableLF()

Value

A list of class availableLF with the components:

Author(s)

Marius D. Pascariu

See Also

MortalityLaw

Examples

availableLF()

Check Available Mortality Laws

Description

The function returns information about the parametric models that can be called and fitted in the MortalityLaw function. For a comprehensive review of the most important mortality laws, Tabeau (2001) is a good starting point.

Usage

availableLaws(law = NULL)

Arguments

Value

The output is of the "availableLaws" class with the following components:

Author(s)

Marius D. Pascariu

References

1. Gompertz, B. (1825). On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies. Philosophical Transactions of the Royal Society of London, 115, 513-583.

2. Makeham, W. (1860). On the Law of Mortality and Construction of Annuity Tables. The Assurance Magazine and Journal of the Institute of Actuaries, 8(6), 301-310. doi:10.1017/S204616580000126X

3. Thiele, T. (1871). On a Mathematical Formula to express the Rate of Mortality throughout the whole of Life, tested by a Series of Observations made use of by the Danish Life Insurance Company of 1871. Journal of the Institute of Actuaries and Assurance Magazine, 16(5), 313-329. doi:10.1017/S2046167400043688

4. Oppermann, L. H. F. (1870). On the graduation of life tables, with special application to the rate of mortality in infancy and childhood. The Insurance Record Minutes from a meeting in the Institute of Actuaries, 42.

5. Wittstein, T. and D. Bumsted. (1883). The Mathematical Law of Mortality. Journal of the Institute of Actuaries and Assurance Magazine, 24(3), 153-173.

6. Steffensen, J. (1930). Infantile mortality from an actuarial point of view. Skandinavisk Aktuarietidskrift 13, 272-286. doi:10.1080/03461238.1930.10416902

7. Perks, W. (1932). On Some Experiments in the Graduation of Mortality Statistics. Journal of the Institute of Actuaries, 63(1), 12-57. doi:10.1017/S0020268100046680

8. Harper, F. S. (1936). An actuarial study of infant mortality. Scandinavian Actuarial Journal 1936 (3-4), 234-270. doi:10.1080/03461238.1936.10405113

9. Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of applied mechanics 103, 293-297. doi:10.1115/1.4010337

10. Beard, R. E. (1971). Some aspects of theories of mortality, cause of death analysis, forecasting and stochastic processes. Biological aspects of demography 999, 57-68.

11. Vaupel, J., Manton, K.G., and Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16(3): 439-454. doi:10.2307/2061224

12. Siler, W. (1979), A Competing-Risk Model for Animal Mortality. Ecology, 60: 750-757. doi:10.2307/1936612

13. Heligman, L., & Pollard, J. (1980). The age pattern of mortality. Journal of the Institute of Actuaries, 107(1), 49-80. doi:10.1017/S0020268100040257

14. Rogers A and Planck F (1983). MODEL: A General Program for Estimating Parametrized Model Schedules of Fertility, Mortality, Migration, and Marital and Labor Force Status Transitions. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-83-102

15. Martinelle S. (1987). A generalized Perks formula for old-age mortality. Stockholm, Sweden, Statistiska Centralbyran, 1987. 55 p. (R&D Report, Research-Methods-Development, U/STM No. 38)

16. Carriere J.F. (1992). Parametric models for life tables. Transactions of the Society of Actuaries. Vol.44

17. Kostaki A. (1992). A nine-parameter version of the Heligman-Pollard formula. Mathematical Population Studies. Vol. 3 277-288. doi:10.1080/08898489209525346

18. Thatcher AR, Kannisto V and Vaupel JW (1998). The force of mortality at ages 80 to 120. Odense Monographs on Population Aging Vol. 5, Odense University Press, 1998. 104, 20 p. Odense, Denmark

19. Tabeau E. (2001). A Review of Demographic Forecasting Models for Mortality. In: Tabeau E., van den Berg Jeths A., Heathcote C. (eds) Forecasting Mortality in Developed Countries. European Studies of Population, vol 9. Springer, Dordrecht. doi:10.1007/0-306-47562-6_1

20. Finkelstein M. (2012) Discussing the Strehler-Mildvan model of mortality Demographic Research, Vol. 26(9), 191-206. doi:10.4054/DemRes.2012.26.9

See Also

MortalityLaw

Examples

availableLaws()

Beard Model - 1971

Description

Beard Model - 1971

Usage

beard(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

beard(x = 50:100)

Makeham-Beard Model - 1971

Description

Makeham-Beard Model - 1971

Usage

beard_makeham(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

beard_makeham(x = 0:100)

Bring or Rename Starting Parameters in the Law Functions

Description

Bring or Rename Starting Parameters in the Law Functions

Usage

bring_parameters(law, par = NULL)

Arguments

Value

Vector or initial model parameters

Carriere Mortality Law - 1992

Description

Carriere1 = weibull + invweibull + gompertz

Usage

carriere1(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

carriere1(x = 0:100)

Carriere Mortality Law - 1992

Description

Carriere2 = weibull + invgompertz + gompertz

Usage

carriere2(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

carriere2(x = 0:100)

Function to check input data in MortalityLaw

Description

Function to check input data in MortalityLaw

Usage

check.MortalityLaw(input)

Arguments

Value

No return value, called for side effects

Check input ReadAHMD

Description

Check input ReadAHMD

Usage

check_input_ReadAHMD(x)

Arguments

Value

No return value, called for checking stuff

Check input for ReadCHMD

Description

Check input for ReadCHMD

Usage

check_input_ReadCHMD(x)

Arguments

Value

No return value, called for input validation

Check input ReadHMD

Description

Check input ReadHMD

Usage

check_input_ReadHMD(x)

Arguments

Value

No return value, called for validating input data

Check input ReadJMD

Description

Check input ReadJMD

Usage

check_input_ReadJMD(x)

Arguments

Value

No return value, called for validating input data

Run the optimisation routine

Description

This is the core optimisation function for MortalityLaw. It:

1. Subsets the data to the fitting ages (fit.this.x).

2. Scales the age vector if required by the chosen model.

3. Obtains default starting parameters (if not provided).

4. Minimises the objective function using nlminb (PORT routines) with the parameters on the log scale.

5. Transforms parameters back to the original scale, computes the fitted hazard, and derives goodness-of-fit measures (AIC, BIC, log-likelihood) where applicable.

Usage

choose_optim(input)

Arguments

Value

A list with components:

Find ax[1:2] indicators using Coale-Demeny coefficients Here we adjust the first two values of ax to account for infant mortality more accurately

Description

Find ax[1:2] indicators using Coale-Demeny coefficients Here we adjust the first two values of ax to account for infant mortality more accurately

Usage

coale.demeny.ax(x, mx, ax, sex)

Arguments

Value

A vector of coefficients

Find ax indicator

Description

Find ax indicator

Usage

compute.ax(x, mx, qx)

Arguments

Value

ax - the point in the age interval where 50 have already occurred

Convert Life Table Indicators

Description

Easily convert between different life table indicators (e.g., from death rates mx to death probabilities qx, or from survivorship lx to life expectancy ex). The function wraps LifeTable internally, so the conversion relies on the same constant-force-of-mortality (CFM) assumption and life-table methodology used throughout the package.

Usage

convertFx(x, data, from, to, ...)

Arguments

Details

This function provides a convenient interface for converting a single mortality indicator into another, without having to call LifeTable directly and extract the desired column.

The supported input types (from) are: mx, qx, dx, and lx.

The supported output types (to) are: mx, qx, dx, lx, Lx, Tx, and ex.

There are 28 possible from-to combinations (4 inputs \times 7 outputs). All conversions pass through the full life-table computation; for example, converting mx to ex will internally compute qx, lx, dx, Lx, and Tx in sequence.

When data is a vector, the function returns a named vector. When data is a matrix or data.frame with multiple columns, the function applies the conversion column-wise and returns a matrix with the same row and column names as the input.

Value

A numeric vector or matrix containing the converted life table indicator. If the input was a named object, the output retains those names.

Author(s)

Marius D. Pascariu

See Also

LifeTable for the underlying life-table construction; LawTable for generating life tables from parametric mortality laws.

Examples

# ---- Basic conversions ----

x  <- 0:110
mx <- ahmd$mx

# Convert death rates to death probabilities
qx <- convertFx(x, data = mx, from = "mx", to = "qx")

# Convert death rates to death distribution
dx <- convertFx(x, data = mx, from = "mx", to = "dx")

# Convert death rates to survivorship
lx <- convertFx(x, data = mx, from = "mx", to = "lx")

# ---- All 28 possible conversions ----

from <- c("mx", "qx", "dx", "lx")
to   <- c("mx", "qx", "dx", "lx", "Lx", "Tx", "ex")
K    <- expand.grid(from = from, to = to)

for (i in 1:nrow(K)) {
  In  <- as.character(K[i, "from"])
  Out <- as.character(K[i, "to"])
  N   <- paste0(Out, "_from_", In)
  cat(i, " Create", N, "\n")
  assign(N, convertFx(x = x, data = get(In), from = In, to = Out))
}

Data formats

Description

Data formats

Usage

data_format()

Value

a vector

deviance function for MortalityLaw

Description

deviance function for MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
deviance(object, ...)

Arguments

Value

model deviance value

df.residual function for MortalityLaw

Description

df.residual function for MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
df.residual(object, ...)

Arguments

Value

model residual value

dx to lx

Description

Function to convert dx into lx and back

Usage

dx_lx(ux, out = c("dx", "lx"))

Arguments

Value

A vector containing dx or lx values

Function that identifies the case/problem we have to solve

Description

Function that identifies the case/problem we have to solve

Usage

find.my.case(Dx = NULL, Ex = NULL, mx = NULL, qx = NULL, lx = NULL, dx = NULL)

Arguments

Value

A list containing problem solving details

Gamma-Gompertz Model as in Vaupel et al. (1979)

Description

Gamma-Gompertz Model as in Vaupel et al. (1979)

Usage

ggompertz(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

ggompertz(x = 50:120)

Gompertz Mortality Law - 1825

Description

Gompertz Mortality Law - 1825

Usage

gompertz(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

gompertz(x = 45:90)

Gompertz Mortality Law - informative parameterization

Description

Gompertz Mortality Law - informative parameterization

Usage

gompertz0(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

gompertz0(x = 45:90)

Summary function - display head and tail in a single data.frame The original code for this function was first written for 'psych' R package here we have modified it a bit

Description

Summary function - display head and tail in a single data.frame The original code for this function was first written for 'psych' R package here we have modified it a bit

Usage

head_tail(x, hlength = 4, tlength = 4, digits = 4, ellipsis = TRUE)

Arguments

Value

Print table's head and tail

Inverse-Gompertz Mortality Law - informative parameterization

Description

m - is a measure of location because it is the mode of the density, m > 0 sigma - represents the dispersion of the density about the mode, sigma > 0

Usage

invgompertz(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

invgompertz(x = 15:25)

Inverse-Weibull Mortality Law

Description

The Inverse-Weibull proves useful for modelling the childhood and teenage years, because the logarithm of h(x) is a concave function. m > 0 is a measure of location sigma > 0 is measure of dispersion

Usage

invweibull(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

invweibull(x = 1:20)

Kannisto Mortality Law - 1998

Description

Kannisto Mortality Law - 1998

Usage

kannisto(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

kannisto(x = 85:120)

Kannisto-Makeham Mortality Law - 1998

Description

Kannisto-Makeham Mortality Law - 1998

Usage

kannisto_makeham(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

kannisto_makeham(x = 85:120)

Kostaki Model - 1992

Description

Kostaki Model - 1992

Usage

kostaki(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

kostaki(x = 0:100)

logLik function for MortalityLaw

Description

logLik function for MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
logLik(object, ...)

Arguments

Value

Model log-likelihood value

Make HTTP request

Description

Make HTTP request

Usage

make_http_request(url)

Arguments

Value

url response

Makeham Mortality Law - 1860

Description

Makeham Mortality Law - 1860

Usage

makeham(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

makeham(x = 45:90)

Makeham Mortality Law - informative parameterization

Description

Makeham Mortality Law - informative parameterization

Usage

makeham0(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

makeham0(x = 45:90)

Martinelle Model - 1987

Description

Martinelle Model - 1987

Usage

martinelle(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

martinelle(x = 0:100)

mx to qx

Description

Function to convert mx into qx and back, using the constant force of mortality assumption (CFM).

Usage

mx_qx(x, nx, ux, out = c("qx", "mx"))

Arguments

Value

A vector of rates

Objective function to minimise during optimisation

Description

Given a set of parameters (on the log scale), this function evaluates the chosen loss function or negative log-likelihood by comparing observed mortality values (Dx/Ex, mx, or qx) against the hazard rates predicted by the specified mortality law.

Usage

objective_fun(par, x, Dx, Ex, mx, qx, law, opt.method, custom.law)

Arguments

Details

Parameters are transformed back to the original scale via exp(par) when calling the mortality law function. Infinite hazard values are capped to 1, and large penalties are applied for missing or out-of-range values to guide the optimiser away from invalid regions.

Value

A scalar loss value to be minimised.

Opperman Mortality Law - 1870

Description

Opperman Mortality Law - 1870

Usage

opperman(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

opperman(x = 1:25)

Perks Model - 1932

Description

Perks Model - 1932

Usage

perks(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

perks(x = 50:100)

Plot Method for MortalityLaw

Description

Plot Method for MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
plot(x, ...)

Arguments

Value

A plot is generated as a side effect.

Author(s)

Marius D. Pascariu

See Also

MortalityLaw

Examples

# See complete example in MortalityLaw help page

Predict function for MortalityLaw

Description

Predict function for MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
predict(object, x, ...)

Arguments

Value

A vector of predicted hazard rates

Author(s)

Marius D. Pascariu

See Also

MortalityLaw

Examples

# Extrapolate old-age mortality with the Kannisto model
# Fit ages 80-94 and extrapolate up to 120.

Mx <- ahmd$mx[paste(80:94), "1950"]
M1 <- MortalityLaw(x = 80:94, mx  = Mx, law = 'kannisto')
fitted(M1)
predict(M1, x = 80:120)

# See more examples in MortalityLaw function help page.

Print LifeTable

Description

Print LifeTable

Usage

## S3 method for class 'LifeTable'
print(x, ...)

Arguments

Value

Print data on the console

Print MortalityLaw

Description

Print MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
print(x, ...)

Arguments

Value

Print data on console

Print ReadCHMD

Description

Print ReadCHMD

Usage

## S3 method for class 'ReadAHMD'
print(x, ...)

Arguments

Value

Print data on console

Print ReadCHMD

Description

Print ReadCHMD

Usage

## S3 method for class 'ReadCHMD'
print(x, ...)

Arguments

Value

Print data on the console

Print ReadHMD

Description

Print ReadHMD

Usage

## S3 method for class 'ReadHMD'
print(x, ...)

Arguments

Value

Print data on the console

Print ReadJMD

Description

Print ReadJMD

Usage

## S3 method for class 'ReadJMD'
print(x, ...)

Arguments

Value

Print info on the console

Print availableLF

Description

Print availableLF

Usage

## S3 method for class 'availableLF'
print(x, ...)

Arguments

Value

print info on the console

Print availableLaws

Description

Print availableLaws

Usage

## S3 method for class 'availableLaws'
print(x, ...)

Arguments

Value

print info on the console

Print summary.MortalityLaw

Description

Print summary.MortalityLaw

Usage

## S3 method for class 'summary.MortalityLaw'
print(x, ...)

Arguments

Value

Print data on console

Quadratic Model

Description

Quadratic Model

Usage

quadratic(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

quadratic(x = 0:100)

Rogers-Planck Model - 1983

Description

Rogers-Planck Model - 1983

Usage

rogersplanck(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

rogersplanck(x = 0:100)

Print message when saving an object

Description

Print message when saving an object

Usage

saveMsg()

Value

No return value, called for side effects

Save Output in the working directory

Description

Save Output in the working directory

Usage

saveOutput(out, show, prefix)

Arguments

Value

No return value, called for side effects

Scale the age vector for stable optimisation

Description

For mortality laws that cover only a portion of the lifespan (e.g., adult or old-age mortality), the age vector is rescaled so that the minimum age becomes 1. This improves numerical stability by keeping the exponentiated terms in the hazard function within a reasonable range.

Usage

scale_x(x)

Arguments

Value

A numeric vector of scaled ages, where min(x) == 1.

Siler Mortality Law - 1979

Description

Siler Mortality Law - 1979

Usage

siler(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

siler(x = 0:100)

Strehler-Mildvan Model - 1960

Description

Strehler-Mildvan Model - 1960

Usage

strehler_mildvan(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

strehler_mildvan(x = 30:85)

Extracting the last n characters from a string

Description

Extracting the last n characters from a string

Usage

substrRight(x, n)

Arguments

Value

A character vector of length n

Summary MortalityLaw

Description

Summary MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
summary(object, ..., digits = max(3L, getOption("digits") - 3L))

Arguments

Value

A list of model diagnosis

Thiele Mortality Law - 1871

Description

Thiele Mortality Law - 1871

Usage

thiele(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

thiele(x = 0:100)

Educate mx or qx on how to behave above age 100 if it gets in trouble (with NA's, zero's and Inf)

Description

Educate mx or qx on how to behave above age 100 if it gets in trouble (with NA's, zero's and Inf)

Usage

uxAbove100(x, ux, omega = 100, verbose = FALSE)

Arguments

Value

A vector of rates

Van der Maen Model - 1943

Description

Van der Maen Model - 1943

Usage

vandermaen(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

vandermaen(x = 0:100)

Van der Maen 2 Model - 1943

Description

Van der Maen 2 Model - 1943

Usage

vandermaen2(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

vandermaen(x = 0:100)

Weibull Mortality Law - 1939

Description

Note that if sigma > m, then the mode of the density is 0 and hx is a non-increasing function of x, while if sigma < m, then the mode is greater than 0 and hx is an increasing function. m > 0 is a measure of location sigma > 0 is measure of dispersion

Usage

weibull(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

weibull(x = 1:20)

Wittstein Mortality Law - 1883

Description

Wittstein Mortality Law - 1883

Usage

wittstein(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

wittstein(x = 0:100)