Gompertz-Makeham parameter estimation - r

Question

I would like estimate the parameters of the Gompert-Makeham distribution, but I haven't got a result.
I would like a method in R, like this Weibull parameter estimation code:
weibull_loglik <- function(parm){
gamma <- parm[1]
lambda <- parm[2]
loglik <- sum(dweibull(vec, shape=gamma, scale=lambda, log=TRUE))
return(-loglik)
}
weibull <- nlm(weibull_loglik,parm<-c(1,1), hessian = TRUE, iterlim=100)
weibull$estimate
c=weibull$estimate[1];b=weibull$estimate[2]
My data:
[1] 872 52 31 26 22 17 11 17 17 8 20 12 25 14 17
[16] 20 17 23 32 37 28 24 43 40 34 29 26 32 34 51
[31] 50 67 84 70 71 137 123 137 172 189 212 251 248 272 314
[46] 374 345 411 494 461 505 506 565 590 535 639 710 733 795 786
[61] 894 963 1019 1149 1185 1356 1354 1460 1622 1783 1843 2049 2262 2316 2591
[76] 2730 2972 3187 3432 3438 3959 3140 3612 3820 3478 4054 3587 3433 3150 2881
[91] 2639 2250 1850 1546 1236 966 729 532 375 256 168 107 65 39 22
[106] 12 6 3 2 1 1
summary(vec)
Min. 1st Qu. Median Mean 3rd Qu. Max.
1.0 32.0 314.0 900.9 1355.0 4054.0

Answer 1

It would be nice to have a reproducible example, but something like:
library(bbmle)
library(eha)
set.seed(101)
vec <- rmakeham(1000, shape = c(2,3), scale = 2)
dmwrap <- function(x, shape1, shape2, scale, log) {
res <- try(dmakeham(x, c(shape1, shape2), scale, log = log), silent = TRUE)
if (inherits(res, "try-error")) return(NA)
res
}
m1 <- mle2(y ~ dmwrap(shape1, shape2, scale),
start = list(shape1=1,shape2=1, scale=1),
data = data.frame(y = vec),
method = "Nelder-Mead"
)
Define a wrapper that (1) takes shape parameters as separate values; (2) returns NA rather than throwing an error when e.g. parameters are negative
Use Nelder-Mead rather than default BFGS for robustness
the fitdistrplus package might help too
if you're going to do a lot of this it may help to fit parameters on the log scale (i.e. use parameters logshape1, etc., and use exp(logshape1) etc. in the fitting formula)
I had to work a little harder to fit your data; I scaled the variable by 1000 (and found that I could only compute the log-likelihood; the likelihood gave an error that I didn't bother trying to track down). Unfortunately, it doesn't look like a great fit (too many small values).
x <- scan(text = "872 52 31 26 22 17 11 17 17 8 20 12 25 14 17
20 17 23 32 37 28 24 43 40 34 29 26 32 34 51
50 67 84 70 71 137 123 137 172 189 212 251 248 272 314
374 345 411 494 461 505 506 565 590 535 639 710 733 795 786
894 963 1019 1149 1185 1356 1354 1460 1622 1783 1843 2049 2262 2316 2591
2730 2972 3187 3432 3438 3959 3140 3612 3820 3478 4054 3587 3433 3150 2881
2639 2250 1850 1546 1236 966 729 532 375 256 168 107 65 39 22
12 6 3 2 1 1")
m1 <- mle2(y ~ dmwrap(shape1, shape2, scale),
start = list(shape1=1,shape2=1, scale=10000),
data = data.frame(y = x/1000),
method = "Nelder-Mead"
)
cc <- as.list(coef(m1))
png("gm.png")
hist(x,breaks = 25, freq=FALSE)
with(cc,
curve(exp(dmwrap(x/1000, shape1, shape2, scale, log = TRUE))/1000, add = TRUE)
)
dev.off()