R version 4.4.0 beta (2024-04-15 r86425 ucrt) -- "Puppy Cup"
Copyright (C) 2024 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> 
> library("mlt")
Loading required package: basefun
Loading required package: variables
> 
> ### 10.1080/15598608.2013.772835
> ### rho = exp(logrho)
> ### 1 = rho = exp(0) is identical to .Logistic
> lg <- mlt:::.GammaFrailty(logrho = 0)
> x <- -30:30 / 20
> p <- 1:99 / 100
> tol <- sqrt(.Machine$double.eps)
> stopifnot(max(abs(lg$p(x) - mlt:::.Logistic()$p(x))) < tol)
> 
> stopifnot(max(abs(lg$d(x) - mlt:::.Logistic()$d(x))) < tol)
> 
> stopifnot(max(abs(lg$dd(x) - mlt:::.Logistic()$dd(x))) < tol)
> 
> stopifnot(max(abs(lg$ddd(x) - mlt:::.Logistic()$ddd(x))) < tol)
> 
> stopifnot(max(abs(lg$dd2d(x) - mlt:::.Logistic()$dd2d(x))) < tol)
> 
> stopifnot(max(abs(lg$q(p) - mlt:::.Logistic()$q(p))) < tol)
> 
> ### 0 = rho = exp(-infty) is identical to .MinExtrVal
> tol <- (.Machine$double.eps)^(1 / 2.5)
> lg <- mlt:::.GammaFrailty(logrho = -18)
> stopifnot(max(abs(lg$p(x) - mlt:::.MinExtrVal()$p(x))) < tol)
> 
> stopifnot(max(abs(lg$d(x) - mlt:::.MinExtrVal()$d(x))) < tol)
> 
> stopifnot(max(abs(lg$dd(x) - mlt:::.MinExtrVal()$dd(x))) < tol)
> 
> stopifnot(max(abs(lg$ddd(x) - mlt:::.MinExtrVal()$ddd(x))) < tol)
> 
> stopifnot(max(abs(lg$dd2d(x) - mlt:::.MinExtrVal()$dd2d(x))) < tol)
> 
> stopifnot(max(abs(lg$q(p) - mlt:::.MinExtrVal()$q(p))) < tol)
> 
> ### logitalpha = logit(1) is identical to .MinExtrVal
> tol <- (.Machine$double.eps)^(1 / 2.5)
> lg <- mlt:::.PositiveStableFrailty(logitalpha = 50)
> stopifnot(max(abs(lg$p(x) - mlt:::.MinExtrVal()$p(x))) < tol)
> 
> stopifnot(max(abs(lg$d(x) - mlt:::.MinExtrVal()$d(x))) < tol)
> 
> stopifnot(max(abs(lg$dd(x) - mlt:::.MinExtrVal()$dd(x))) < tol)
> 
> stopifnot(max(abs(lg$ddd(x) - mlt:::.MinExtrVal()$ddd(x))) < tol)
> 
> stopifnot(max(abs(lg$dd2d(x) - mlt:::.MinExtrVal()$dd2d(x))) < tol)
> 
> stopifnot(max(abs(lg$q(p) - mlt:::.MinExtrVal()$q(p))) < tol)
> 
> 
> proc.time()
   user  system elapsed 
   0.92    0.09    1.00