# [R] Maximum likelihood estimation

toh tohbin at yahoo.com
Thu Sep 4 08:33:21 CEST 2008

```Hi R-experts,
I'm new to R in mle. I tried to do the following but just couldn't get it
right. Hope someone can point out the mistakes. thanks a lot.

t <- c(1:90)
y <-
c(5,10,15,20,26,34,36,43,47,49,80,84,108,157,171,183,191,200,204,211,217,226,230,

234,236,240,243,252,254,259,263,264,268,271,277,290,309,324,331,346,367,375,381,

401,411,414,417,425,430,431,433,435,437,444,446,446,448,451,453,460,463,463,464,

464,465,465,465,466,467,467,467,468,469,469,469,469,470,472,472,473,473,473,473,
473,473,473,475,475,475,475)
fr <- function(a, b, p, lambda){
l <- 0.5*(lambda + b*p + (1-p)*(lambda-b))
l^2 > lambda*b*p
delta <- sqrt(abs(l^2 - b*p*lambda))
mt <- a/p*(1-exp(-l*t)*cosh(delta*t)-(l-b*p)*exp(-t)*sinh(delta*t)/delta)
logl <- sum(diff(y)*log(diff(mt))-diff(mt)-lfactorial(diff(y)))
return(-logl)
}
optim(c(15,0.01,0.5,0.01),fr, method="L-BFGS-B",
lower = c(0.002, 0.002, 0.002, 0.002), upper = c(Inf, Inf, 0.999,
Inf),control=list(fnscale=-1))

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```