Binomial likelihood for a set of Heligman-Pollard Parameters

Description

Calculates the log-likelihood based on a binomial distribution of observing a set of age-specific probabilities of death resulting from a set of eight parameters of the Heligman-Pollard Model given a certain number of age-specific death counts and persons at risk

Usage

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mp8.ll(theta, nrisk, ndeath, age = c(1e-05, 1, seq(5, 85, 5)))

Arguments

theta

A vector containing the values for the 8 Heligman-Pollard parameters

nrisk

A vector containing the number of persons at risk in each age group

ndeath

A vector containing the number of deaths in each age group

age

A vector containing the age values of which the probabilities of death resulting from the HP model are a function

Value

Log likelihood of observing the resulting probabilities of death calculated from the set of parameters, theta

Note

For use in the optimizer step of the IMIS procedure

References

Heligman, Larry and John H. Pollard. 1980 "The Age Pattern of Mortality." Journal of the Institute of Actuaries 107:49–80.

See Also

loop.optim, hp.bm.imis

Examples

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##A set of parameters##
theta <- c(0.06008, 0.31087, 0.34431, 0.00698,
           1.98569, 26.71071, 0.00022, 1.08800)
##Deaths and persons at risk##
lx <- c(1974, 1906, 1860, 1844, 1834, 1823, 1793, 1700, 1549, 1361, 
1181, 1025, 870, 721, 571, 450, 344, 256, 142, 79, 41, 8)
dx <- c(68, 47, 16, 10, 13, 29, 92, 151, 188, 179, 156, 155, 147, 150, 
122, 106, 88, 113, 63, 38, 32, 8)
mp8.ll(theta=theta, nrisk=lx, ndeath=dx)