R Under development (unstable) (2024-07-10 r86888 ucrt) -- "Unsuffered Consequences"
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> library(fitdistrplus)
Loading required package: MASS
Loading required package: survival
> 
> 
> 
> set.seed(1234)
> nsample <- 10
> 
> 
> # (1) uniform distribution fit - no fixed value
> 
> #manual check
> dunif2 <- function(x, min, max)
+   dunif(x, min, max)
> punif2 <- function(q, min, max)
+   punif(q, min, max)
> 
> x1 <- runif(nsample, 3, 5)
> 
> L <- function(a, b, obs)
+   prod(dunif(obs, min=a, max=b))
> l <- Vectorize(L, "a")
> curve(l(x, b=5, obs=x1), from=1, to=3)
> 
> f1 <- fitdist(x1, "unif")
> f2 <- fitdist(x1, "unif2", start=list(min=0, max=10), lower=c(-Inf, max(x1)),
+               upper=c(min(x1), Inf))
> c(logLik(f1), logLik(f2))
[1] -5.322970 -5.323165
> 
> delta <- .2
> llsurface(x1, "unif", plot.arg = c("min", "max"), min.arg=c(1, 5-delta),
+           max.arg=c(3+delta, 7), main="likelihood surface for uniform")
> abline(v=3, h=5, col="red", lty=2)
> points(f1$estimate[1], f1$estimate[2], pch="x", col="violet")
> points(f2$estimate[1], f2$estimate[2], pch="o", col="blue")
> 
> # (2) uniform distribution fit - fixed value
> 
> f3 <- fitdist(x1, "unif", fix.arg=list(min=2.5))
> logLik(f3)
[1] -7.983315
> 
> llcurve(x1, "unif", plot.arg="max", min.arg = 5-delta, max.arg=7)
> 
> f4 <- fitdist(x1, "unif", fix.arg=list(max=5.5))
> logLik(f4)
[1] -9.086651
> 
> 
> # (3) four parameter beta - also known as PERT distribution
> require(mc2d)
Loading required package: mc2d
Loading required package: mvtnorm

Attaching package: 'mc2d'

The following objects are masked from 'package:base':

    pmax, pmin

> 
> x2 <- rpert(2*nsample, 0, 1, 2, 3)
> 
> f1 <- fitdist(x2, "pert", start=list(min=-1, mode=0, max=10, shape=1),
+               lower=c(-Inf, -Inf, max(x2), 0),
+               upper=c(min(x2), Inf, Inf, Inf))
Warning messages:
1: In cov2cor(varcovar) :
  diag(V) had non-positive or NA entries; the non-finite result may be dubious
2: In sqrt(diag(varcovar)) : NaNs produced
> f2 <- fitdist(x2, "pert", start=list(mode=1, shape=1), 
+               lower=c(-Inf, 0),
+               upper=c(Inf, Inf),
+               fix.arg=list(min=min(x2)-1e-6, max=max(x2)+1e-6))
Warning messages:
1: In cov2cor(varcovar) :
  diag(V) had non-positive or NA entries; the non-finite result may be dubious
2: In sqrt(diag(varcovar)) : NaNs produced
> 
> gofstat(list(f1,f2))
Goodness-of-fit statistics
                             1-mle-pert 2-mle-pert
Kolmogorov-Smirnov statistic  0.1767997  0.3074253
Cramer-von Mises statistic    0.0706553  0.3671139
Anderson-Darling statistic    0.3920664  2.6203988

Goodness-of-fit criteria
                               1-mle-pert 2-mle-pert
Akaike's Information Criterion   10.46162   8.877349
Bayesian Information Criterion   14.44455  10.868814
> cdfcomp(list(f1,f2))
> 
> proc.time()
   user  system elapsed 
   2.59    0.50    3.07