手动对数似然与 logLike 函数之间的区别

Question

我正在尝试比较 logLik 函数给出的对数似然函数的值和手动计算的 Gamma 分布值。 logLik函数给出的值为：

require(fitdistrplus)

x = rgamma(50,shape = 2, scale = 10)
Gamma_fitdist = fitdist(x,"gamma")
logLik(Gamma_fitdistr)
-189.4192

“手动”对数似然函数是：

gmll <- function(scale,shape,datta){
  a <- scale
  b <- shape
  n <- length(datta)
  sumd <- sum(datta)
  sumlogd <- sum(log(datta))
  gmll <- n*a*log(b) + n*lgamma(a) + sumd/b - (a-1)*sumlogd
  gmll
} 

gmll(scale = 10, shape = 2, datta = x)
-246.6081

为什么 logLik 函数给我不同的值？谢谢！

Answer 1

你颠倒了比例和形状，你的代码中有几个符号错误。

library(fitdistrplus)

set.seed(666)
x = rgamma(50, shape = 2, scale = 4)

Gamma_fitdist = fitdist(x,"gamma")
logLik(Gamma_fitdist)
# -150.3687

gmll <- function(scale,shape,datta){
  a <- shape
  b <- scale
  n <- length(datta)
  sumd <- sum(datta)
  sumlogd <- sum(log(datta))
  -n*a*log(b) - n*lgamma(a) - sumd/b + (a-1)*sumlogd
} 

rate <- Gamma_fitdist$estimate[["rate"]]
shape <- Gamma_fitdist$estimate[["shape"]]
gmll(scale = 1/rate, shape = shape, datta = x)
# -150.3687

手动对数似然与 logLike 函数之间的区别

Difference between log likelihood by hand and logLike function

statistics

r

log-likelihood