MLE无法估计错误代码为7的参数

Question

我正在尝试估计Weibull-Gamma分布参数，但是遇到以下错误：

“函数mle无法估计参数，错误代码为7”我该怎么办？

Weibull-Gamma分布

密度函数

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

累计功能

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

Harzard函数

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)) 
}

生存功能

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

估算

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

[https://i.stack.imgur.com/XDxwC.png][1]图片

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)

Answer 1

对于您的样本，估计ML时算法不会收敛。将Weibull-Gamma分布拟合到此数据将需要极高的lambda值。您可以通过估算log10(lambda)而不是lambda来解决此问题。

您可以在4个函数中添加lambda <- 10^lambda，例如

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

然后，该算法似乎收敛了：

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

输出：

     alpha       beta     lambda 
  2.432939 799.631852   8.680802 

我们看到lambda的估计为10^8.68，因此在不获取对数时会出现收敛问题。

您也可以按照以下方式查看其拟合度：

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)

注意：也许适合其他发行版会更有意义？