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MortalityLaws hex logo MortalityLaws: Parametric Mortality Models, Life Tables and HMD

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A mortality law is a small parametric function that describes how a population dies out with age: high mortality in infancy, a hump at young adult ages, and an exponential climb from middle age onward. MortalityLaws fits these laws to observed deaths, exposures and rates, turns any fit or any observed schedule into a full life table, and pulls the underlying data straight from the Human Mortality Database and its national siblings.

The problem this solves

Mortality data rarely arrive in the shape the question needs. A statistical office publishes deaths and exposures by age and year. The resulting curve is jagged where deaths are few, thin at the oldest ages, and often closed at 85+ or 90+ with a single wide interval. What you usually want is the opposite: a smooth description of the age pattern of death that you can compare across populations and years, integrate into a life table, or carry past the last observed age.

Parametric mortality laws are the classical answer, and there are many of them. Each is a small formula with a handful of parameters, each is good at some part of the age range and quietly wrong somewhere else. Doing this by hand means a spreadsheet of starting values, one script per formula, and no two fits graduated quite the same way. (Picking a law by eye is a time-honoured tradition, and reproducible only by accident.)

MortalityLaws removes the assembly line. The package ships 38 laws, 8 fitting objectives (two likelihoods and six losses) and 6 accepted life-table inputs. That is 38 x 8 x 6 = 1,824 combinations of law, loss and input, and every one of them is a single function call.

From one observed curve to a whole life table

Age-specific death rates of England and Wales females in 1950 as black crosses on a log scale, with four fitted laws overlaid on the left (Heligman-Pollard and Siler over ages 0-100, Kannisto-Makeham over ages 60-100 and Gompertz over ages 40-80), and on the right the life table the fit implies: survivorship l(x) with radix 100,000 and life expectancy e(x) from a LawTable built on the Heligman-Pollard fit.
Age-specific death rates of England and Wales females in 1950 as black crosses on a log scale, with four fitted laws overlaid on the left (Heligman-Pollard and Siler over ages 0-100, Kannisto-Makeham over ages 60-100 and Gompertz over ages 40-80), and on the right the life table the fit implies: survivorship l(x) with radix 100,000 and life expectancy e(x) from a LawTable built on the Heligman-Pollard fit.

What it does

capability how
Fit a law to observed data MortalityLaw(), from deaths and exposures, mx, or qx
Supply your own law custom.law, any function of x and par you can write
Judge whether a fit deserves trust plot.MortalityLaw(): observed versus fitted, plus four residual diagnostics
Build full and abridged life tables LifeTable(): 6 input types, 4 ax methods, and close / omega for the tail
Convert between mortality indicators convertFx() across mx, qx, dx, lx, Lx, Tx, ex; LawTable() turns a law and its parameters into a whole table
Download demographic data ReadHMD(), ReadJMD(), ReadCHMD(), ReadAHMD(): 50 HMD countries, 6 interval formats from 1x1 to 5x10
Look things up availableLaws(), availableLF(), availableHMD(), dispersion()

Installation

Install the stable release from CRAN:

install.packages("MortalityLaws")

The development version comes from GitHub. pak is the recommended installer, and like any install from source it needs a working development toolchain:

# install.packages("pak")
pak::pak("mpascariu/MortalityLaws")

Check that everything works:

library(MortalityLaws)
availableLaws()   # the catalogue: 38 laws with formulas and lifespan types

Updating

For the CRAN version, simply re-run install.packages("MortalityLaws") every so often. For the development version, run pak::pak("mpascariu/MortalityLaws") again to pull the latest commits.

Documentation

Citation

To cite MortalityLaws in publications use:

Pascariu M (2026). MortalityLaws: Parametric Mortality Models, Life Tables and HMD. R package version 3.0.0, https://github.com/mpascariu/MortalityLaws.

A BibTeX entry for LaTeX users is:

  @Manual{,
    title = {MortalityLaws: Parametric Mortality Models, Life Tables and HMD},
    author = {Marius D. Pascariu},
    year = {2026},
    note = {R package version 3.0.0},
    url = {https://github.com/mpascariu/MortalityLaws},
  }

Contributing

Issues and pull requests are welcome. If MortalityLaws misbehaves, please open an issue with a minimal reproducible example at https://github.com/mpascariu/MortalityLaws/issues, and see CONTRIBUTING.md. This project is released with a Contributor Code of Conduct.