R Under development (unstable) (2023-06-29 r84618 ucrt) -- "Unsuffered Consequences"
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> 
> 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 
   1.59    0.32    1.84