mle failed to estimate the parameters with the error code 7

I'm trying to estimate the Weibull-Gamma Distribution parameters, but I'm encountering the following error:

"the function mle failed to estimate the parameters, with the error code 7"

What do I do?

The Weibull-Gamma Distribution

Density Function

dWeibullGamma <- function(x, alpha, beta, lambda) 
{
  ((alpha*beta)/(lambda))*(x^(alpha-1))*(1+(1/lambda)*x^(alpha))^(-(beta+1))
}

Cumulative Distribution Function

   pWeibullGamma <- function(x, alpha, beta, lambda) 
{
  1-(1+(1/lambda)*x^(alpha))^(-(beta))
}

Hazard Function

hWeibullGamma <- function(x, alpha, beta, lambda) 
{
((alpha*beta)/(lambda))*(x^(alpha-1))*(1+(1/lambda)*x^(alpha))^(-(beta+1))/(1+(1/lambda)*x^(alpha))^(-(beta)) 
}

Survival Function

sWeibullGamma <- function(x,alpha,beta,lambda)
{
  (1+(1/lambda)*x^(alpha))^(-(beta))
}

Estimation

paramWG = fitdist(data = dadosp, distr = 'WeibullGamma', start = c(alpha=1.5,beta=1,lambda=1.5), lower= c(0, 0))
summary(paramWG) 

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)

For your sample, the algorithm does not converge when estimating the ML. Fitting a Weibull-Gamma distribution to this data would require an extremely high lambda value. You can solve this problem by estimating log10(lambda) instead of lambda.

You can add lambda <- 10^lambda inside your 4 functions, e.g.

dWeibullGamma <- function(x, alpha, beta, lambda) 
{
  lambda <- 10^lambda
  ((alpha*beta)/(lambda))*(x^(alpha-1))*(1+(1/lambda)*x^(alpha))^(-(beta+1))
}

Then, the algorithm seems to converge:

library(fitdistrplus)
paramWG = fitdist(data = data, distr = 'WeibullGamma',
                  start = list(alpha=1, beta=1, lambda=1), lower = c(0, 0, 0))
summary(paramWG)$estimate

Output:

     alpha       beta     lambda 
  2.432939 799.631852   8.680802 

We see that the estimate of lambda is 10^8.68, hence the convergence problem when not taking the log.

You can also have a look at the fit as follows:

newx <- 0:500
pars <- summary(paramWG)$estimate
pred <- dWeibullGamma(newx, pars["alpha"], pars["beta"], pars["lambda"])

hist(data, freq = FALSE)
lines(newx, pred, lwd = 2)

Note: maybe fitting another distribution would make more sense?