I am trying to find the optimum of a function:
I have the following function which I want to fine your
minimum(clearly there is a minumum):
ob<
function(alpha, beta)
{
(1 * (N * log(alpha) + (N * alpha  1) * log(beta)  (alpha  1) *
sum(log(beta + x))))/N
}
I have also the gradient and hessian matrix in the list:
grad <
function(alpha, beta)
{
list(gradient = c(1/alpha  log(beta) + sum(log(beta + x))/N,  (N *
alpha  1)/(N * beta) + ((alpha
+
1) * sum(1/(beta + x)))/N), hessian = c(1/(alpha^2), 1/beta +
sum(1/(beta  x))/N, (N * alpha

1)/(N * beta^2)  ((alpha + 1) * sum(1/((beta + x)^2)))/N))
}
WHERE: 0<alpha<1
0<beta<infinity
M=52 and N=30 (both avaliable in working directory)
x=c(49, 5, 17, 2, 39, 84, 7, 0, 35, 36, 1400, 5, 34, 15,
11, 2, 1, 39, 8, 101, 2, 148, 1, 68,
31, 1, 20, 118, 91, 427) (avaliable in working
directory)
So, I put the command:
nlminb(st = c(0.4, 5), objective = ob, gradient = grad, hessian = T, ,
N = N, M = M, x = x)
$parameters:
[1] 0.4 5.0
$objective:
[1] 0
$message:
NULL
$grad.norm:
[1] 0
$iterations:
[1] 0
$f.evals:
[1] 1
$g.evals:
[1] 1
$hessian:
[,1] [,2]
[1,] 0 0
[2,] 0 0
$scale:
[1] 1 1
$aux:
$aux$N:
[1] 30
$aux$M:
[1] 52
$aux$x:
[1] 49 5 17 2 39 84 7 0 35 36 1400 5 34
15 11 2 1 39 8 101 2
[22] 148 1 68 31 1 20 118 91 427
$call:
nlminb(start = c(0.4, 5), objective = ob, gradient = grad, hessian = T,
N = N, M = M, x = x)
Warning messages:
1: Condition has 2 elements: only the first used in: is.na(fx) 
is.nan(fx)
2: singularity encountered in: nlminb.2(temp, p, liv, lv, lh, objective,
gradient, bounds)
Do I making any error???
Thanks!

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