如何使用“maxlik”包估计广义指数函数的尺度和形状参数？

Question

I want to test the closeness of my sample data with the Generalized Exponential (GE) distribution. For that, I am using ks test in R. In the documentation of ks.gen.exp (reliaR package), its is given : ## Estimates of alpha & lambda using 'maxLik' package. Example code from R package reliaR

## Load data sets
data(bearings)
## Estimates of alpha & lambda using 'maxLik' package
## alpha.est = 5.28321139, lambda.est = 0.03229609
ks.gen.exp(bearings, 5.28321139, 0.03229609, alternative = "two.sided", plot = TRUE)

Can anyone tell me how to estimate alpha(shape parameter) and lambda(scale parameter) using maxLik package?

Answer 1

This is not the most elegant solution but following the examples found in ?maxLik , the code below is one such solution. Note that the method "BFGS" may (not) be the best, but it reproduced the results of the example in ?ks.gen.exp .

loglik.genExp <- function(theta){

    # Just incase you don't want to give the input names
    if(is.null(names(theta))){
        names(theta) <- c("alpha", "lambda")
    }

    # generate a numeric vector of probability densities from a general
    # exponential distribution
    rrgs <- c(list(x = z), as.list(theta))
    l    <- do.call("dgen.exp", rrgs)

    # return the log-likelihood
    sum(log(l))
}

# Assign your sample to the variable z
z <- bearings
maxLik(logLik = loglik.genExp, start = c(5.3, 0.03), method = "BFGS")