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Modified Weibull Error - the function failed to estimate the parameters, with the error code 100

I'm trying to estimate the Almalki and Yuan's modified Weibull distribution (NMW) parameters, but I'm encountering the following error:

The value of the AIC is giving negative ONLY VERY NEGATIVE. Something is wrong. I know that in the literature the AIC may be negative, but I believe that some error in the estimation or the functions is happening. Can the bug be in the estimation, fitdist or something like that? Somebody help me?

ARTICLE

 https://www.sciencedirect.com/science/article/pii/S0951832012002396

Acumulative Function 

  pnmw = function(x, alpha, beta, gama,theta, lambda)
{
  1 - exp(-alpha*(x^(theta))-beta*(x^(gama))*exp(lambda*x))
}

Density Function

       dnmw = function(x, alpha, beta, gama, theta, lambda)
{
  (alpha * theta * (x^(theta - 1)) + beta*(((gama+lambda*x)*(x^(gama-1))*exp(lambda*x))*exp(-alpha*x^(theta)-beta*x^(gama)*exp(lambda*x)))) 
}

Harzard Function 

   hnmw = function(x, alpha, beta, gama, theta, lambda)
{
  alpha * theta * x^(theta - 1) + beta * (gama  + lambda * x) * 
    x^(gama - 1) * exp(lambda * x)
}

Survival Function

   snmw = function(x, alpha, beta, gama, theta, lambda)
{
  exp(-alpha*x^(theta)-beta*x^(gama)*exp(lambda*x))
}

Estimation

paramYuan = fitdist(data = dadosp, distr = 'nmw', start = c(0.05,5,1.25,5,0.05),lower = c(0, 0))

IMAGES

 [https://i.sstatic.net/XDxwC.png][1] Image
    [https://i.sstatic.net/87Cid.png][1] Image Estimation
    [https://i.sstatic.net/FScsM.png][3] Image Functions

Sample: 

    dadosp = c(240.3,71.9,271.3, 186.3,241,253,287.4,138.3,206.9,176,270.4,73.3,118.9,203.1,139.7,31,269.6,140.2,205.1,133.2,107,354.6,277,27.6,186,260.9,350.4,242.6,292.5, 112.3,242.8,310.7,309.9,53.1,326.5,145.7,271.5, 117.5,264.7,243.9,182,136.7,103.8,188.3,236,419.8,338.6,357.7)

[https://i.sstatic.net/U0KwD.png][1] IMAGE

Solution

  • Let's do a little testing with your effort at a density function.

    dnmw = function(x, alpha, beta, gama, theta, lambda)
   {
(alpha * theta * (x^(theta - 1)) + beta*(((gama+lambda*x)*(x^(gama-1))*exp(lambda*x))*
     exp(-alpha*x^(theta)-beta*x^(gama)*exp(lambda*x)))) 
    }
 curve(dnmw(x,4,.3,2.4,2,0.05))

    enter image description here

    I think we need to conclude that this is NOT a good density function since it's integral is clearly greater than 1. Also look at the documentation: http://uksacb.org/sites/default/files/webform/Research%20Paper1_A%20new%20modi%EF%AC%81ed%20Weibull%20distribution_0.pdf

    So take the code and put it into an R-aware editor and see where the match to the rightmost paren might be:

    dnmw = function(x, alpha, beta, gama, theta, lambda)
{
(alpha * theta * (x^(theta - 1)) + beta*(((gama+lambda*x)*(x^(gama-1))*exp(lambda*x))*
#^
             exp(-alpha*x^(theta)-beta*x^(gama)*exp(lambda*x)))) 
#                                                              ^
}

    It matched with the one to the extreme left! But that left-paren was supposed to be matching the one just to the right of exp(lambda*x) to fence off what I would call the normalization terms. So put a right paren in that spot and try to figure out where there is a missing paren elsewhere. .... After several corrections, we get:

    dnmw = function(x, alpha, beta, gama, theta, lambda)
{
  (alpha*theta*(x^(theta - 1)) +beta*( (gama+lambda*x) * x^(gama-1)*
  exp(lambda*x) ))*exp(-alpha*x^(theta)-beta*x^(gama)*exp(lambda*x))
}

    enter image description here

    And now things look more sensible when examining a graphical test. But I also think you need to make sure your other distribution functions do not have similar errors.