R Under development (unstable) (2025-06-30 r88369 ucrt) -- "Unsuffered Consequences"
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> require("fitdistrplus")
Loading required package: fitdistrplus
Loading required package: MASS
Loading required package: survival
> nsample <- 1000
> nsample <- 10
> 
> 
> #(1) beta distribution
> #
> 
> x <- rbeta(nsample, 3, 3/4)
> 
> llsurface(data = x, distr = "beta", plot.arg=c("shape1", "shape2"),
+           min.arg=c(0.1, 0.1), max.arg=c(7, 3))
> llsurface(data = x, distr = "beta", plot.arg=c("shape1", "shape2"),
+           min.arg=c(0.1, 0.1), max.arg=c(7, 3), back.col = FALSE )
> points(3, 3/4, pch="+", col="red")
> 
> 
> llcurve(data = x, distr = "beta", plot.arg = "shape1", min.arg = 0.1, max.arg = 7, 
+         fix.arg = list(shape2 = 3/4), lseq=100, col = "blue")
> llcurve(data = x, distr = "beta", plot.arg = "shape2", min.arg = 0.1, max.arg = 7, 
+         fix.arg = list(shape1 = 3), lseq=100, col = "red")
> 
> 
> 
> 
> #test
> 
> psi <- function(x) digamma(x)
> 
> grbetalnl <- function(x, a, b)
+   c(log(x)-psi(a)+psi(a+b), log(1-x)-psi(b)+psi(a+b))
> 
> grbetalnl(x, 3, 4)
 [1]  0.87613420 -0.35048197  0.94684135  0.52082585  0.92596452  0.07772637
 [7]  0.94935142 -0.76656641  0.91099077  0.35341876 -2.02554426  0.29866219
[13] -5.14252122 -0.43615005 -3.12355125  0.07538168 -6.72437889  0.41860340
[19] -2.64673146 -0.18337799
> 
> grlnL <- function(par, obs, ...) 
+   -rowSums(sapply(obs, function(x) grbetalnl(x, a=par[1], b=par[2])))
> 
> rowSums(sapply(x, function(x) grbetalnl(x, 3, 4)))
[1]   4.444205 -19.489608
> grlnL(c(3, 4), x)
[1] -4.444205 19.489608
> grlnL(c(3, 3/4), x)
[1] 2.458265 2.972292
> 
> 
> ctr <- list(trace=0, REPORT=1, maxit=1000)
> 
> bfgs_gr <- mledist(x, dist="beta", optim.method="BFGS", gr=grlnL, control=ctr)
> bfgs <- mledist(x, dist="beta", optim.method="BFGS", control=ctr)
> 
> cg_gr <- mledist(x, dist="beta", optim.method="CG", gr=grlnL, control=ctr)
> cg <- mledist(x, dist="beta", optim.method="CG", control=ctr)
> 
> nm_gr <- mledist(x, dist="beta", optim.method="Nelder", gr=grlnL, control=ctr)
> nm <- mledist(x, dist="beta", optim.method="Nelder", control=ctr)
> 
> getval <- function(x)
+   c(x$estimate, loglik=x$loglik, x$counts)
> 
> cbind(NM=getval(nm), NMgrad=getval(nm_gr), CG=getval(cg), 
+       CGgrad=getval(cg_gr), BFGS=getval(bfgs), BFGSgrad=getval(bfgs_gr))
                 NM     NMgrad          CG      CGgrad      BFGS   BFGSgrad
shape1    0.9993314  0.9993314   0.9993461   0.9993472 0.9993548  0.9993470
shape2    0.3897140  0.3897140   0.3896660   0.3896655 0.3896650  0.3896652
loglik    6.2342447  6.2342447   6.2342448   6.2342448 6.2342448  6.2342448
function 41.0000000 41.0000000 113.0000000 106.0000000 9.0000000 20.0000000
gradient         NA         NA  47.0000000  33.0000000 6.0000000  5.0000000
> 
> 
> 
> llsurface(data = x, distr = "beta", plot.arg = c("shape1", "shape2"),
+           min.arg = c(0.1, 0.1), max.arg = c(7, 3), pal.col = heat.colors(50))
> points(bfgs$estimate[1], bfgs$estimate[2], pch="+", col="red")
> points(3, 3/4, pch="x", col="green")
> 
> 
> 
> proc.time()
   user  system elapsed 
   1.70    0.23    1.92