# pri.mle: Heligman-Pollard parameter prior formation for use with... In HPbayes: Heligman Pollard mortality model parameter estimation using Bayesian Melding with Incremental Mixture Importance Sampling

## Description

Forms a prior distribution (drawn from a uniform distribution) for each of the eight Heligman-Pollard parameters. First, using `optim()`, mle estimates of the parameters are fitted to the deaths and persons at risk supplied by the user. Once these estimates (returned as `mle`) and their standard errors (`se`) are obtained, 8000 (See documentation for `prior.form`) draws from a uniform distribution with bounds `mle[i] +/- senum*se` are taken to form a prior distribution for each parameter.

## Usage

 ```1 2 3 4 5``` ```pri.mle(nrisk, ndeath, age = c(0, 1, seq(5, 100, 5)), lo = c(1e-08, 1e-07, 1e-07, 1e-07, 1e-07, 15, 1e-07, 1), hi = c(1, 1, 1, 0.5, 15, 55, 0.1, 1.5), senum = 15, theta.test = c(0.06008, 0.31087, 0.34431, 0.00698, 1.98569, 26.71071, 0.00022, 1.088), opt.meth = "Nelder-Mead") ```

## Arguments

 `nrisk` The number of persons at risk of death in each age group `ndeath` The number of deaths in each age group `age` A vector containing the ages at which probabilities of death are calculated `lo` If `opt.meth="L-BFGS"`, this vector contains the lower bounds in `lower` argument of `optim()` ) `hi` If `opt.meth="L-BFGS"`, this vector contains the upper bounds in `upper` argument of `optim()` ) `senum` The number of standard errors on each side of the mle estimate. This argument controls how wide or narrow the uniform distribution is from which the prior distribution will be drawn. `theta.test` Start values for optim. The defaults encompass the Brass standard (Rogers and McKnown 1989). `opt.meth` The same as `method` in `opim()`.

## Details

Priors drawn with this function can be used with the function `hp.bm.imis` or other functions from the HPbayes package.

## Value

 `q0` A matrix containing the prior distibution with each column corresponding to one of the Heligman-Pollard parameters `mle` A vector containing the mle estimates. These define the center of each uniform from which the prior was drawn `se.out` A vector containing the standard error for each element of `mle` `pri.lo` The lower bounds on the uniform distributions from which the prior for each parameter is drawn `pri.hi` The upper bounds on the uniform distributions from which the prior for each parameter is drawn

## References

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

`hp.bm.imis`, `optim`

## Examples

 ```1 2 3``` ```data(HPprior) ##loads a vector of persons at risk (lx) and deaths (dx) prior <- pri.mle(nrisk=lx, ndeath=dx) summary(prior\$q0) ```

### Example output

```Loading required package: MASS
V1                  V2                  V3                  V4
Min.   :0.0001302   Min.   :0.0000444   Min.   :0.0003276   Min.   :0.06964
1st Qu.:0.2502558   1st Qu.:0.2502829   1st Qu.:0.2506613   1st Qu.:0.11589
Median :0.4968367   Median :0.4929713   Median :0.4982379   Median :0.16159
Mean   :0.5002196   Mean   :0.4992367   Mean   :0.4988832   Mean   :0.16128
3rd Qu.:0.7541943   3rd Qu.:0.7578645   3rd Qu.:0.7487897   3rd Qu.:0.20659
Max.   :0.9998715   Max.   :0.9999158   Max.   :0.9998900   Max.   :0.25220
V5                 V6              V7                  V8
Min.   :0.000495   Min.   :17.87   Min.   :1.089e-07   Min.   :1.115
1st Qu.:1.390932   1st Qu.:27.27   1st Qu.:3.977e-05   1st Qu.:1.129
Median :2.732871   Median :36.67   Median :7.860e-05   Median :1.143
Mean   :2.749613   Mean   :36.48   Mean   :7.853e-05   Mean   :1.143
3rd Qu.:4.116821   3rd Qu.:45.65   3rd Qu.:1.185e-04   3rd Qu.:1.157
Max.   :5.478265   Max.   :54.99   Max.   :1.555e-04   Max.   :1.172
```

HPbayes documentation built on May 29, 2017, 6:46 p.m.