# mp8.ll: Binomial likelihood for a set of Heligman-Pollard Parameters In HPbayes: Heligman Pollard mortality model parameter estimation using Bayesian Melding with Incremental Mixture Importance Sampling

## 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

 `1` ```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.

`loop.optim`, `hp.bm.imis`
 ```1 2 3 4 5 6 7 8 9``` ```##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) ```