零膨胀泊松分布：无法估计参数，错误代码为 100

Question

以下是我正在处理的一种数据集：

data <- c(0, 1, 0, 11, 2, 0, 3, 0, 0, 2, 1, 3, 1, 0, 1, 0, 0, 0, 2, 3, 
0, 0, 0, 8, 1, 1, 1, 0, 1, 1, 2, 7, 0, 0, 0, 5, 2, 3, 6, 1, 1, 
5, 2, 9, 0, 0, 1, 21, 16, 2, 9, 6, 25, 2, 1, 12, 16, 14, 15, 
15, 6, 1, 12, 12, 13, 5, 5, 6, 4, 7, 11, 8, 4, 5, 8, 3, 8, 4, 
7, 4, 7, 2, 5, 6, 4, 5, 1, 0, 8, 5, 6, 8, 9, 8, 9, 7, 7, 9, 8, 
9, 4, 4, 7, 13, 9, 13, 12, 10, 9, 8, 7, 11, 5, 5, 0, 1, 33, 4, 
22, 19, 22, 9, 5, 4, 17, 7, 7, 4, 5, 3, 0, 0, 9, 3, 0, 0, 36, 
40, 5, 4, 0, 11, 0, 7, 5, 25, 39, 26, 4, 20, 12, 4, 17, 3, 22, 
12, 14, 8, 9, 11, 7, 11, 10, 9, 16, 6, 24, 8, 5, 6, 14, 3, 9, 
4, 1, 20, 0, 1, 7, 9, 0, 12, 2, 29, 56, 16, 8, 28, 0, 19, 25, 
35, 87, 56, 66, 60, 58, 14, 10, 12, 13, 13, 34, 26, 18, 13, 22, 
13, 12, 15, 41, 11, 11, 11, 5, 6, 7, 8, 8, 17, 16, 12, 21, 38, 
34, 10, 77, 41, 7, 12, 1, 16, 20, 8, 5, 2, 20, 7, 16, 12, 6, 
10, 31, 12)

我使用了fitdistrplus 包来使用最大似然拟合分布。
同样，gamlss 包定义了零膨胀泊松分布的 pdf、CDF。

library(fitdistrplus)   
library(gamlss)  

这是数据集的均值和标准差。

mu=mean(data)
sigma=sd(data)

数据集的平均值为 10.75，标准差为 13.050。我尝试使用 fitdist 函数拟合零膨胀泊松分布，如下所示。

fit_zip = fitdist(data, 'ZIP', start = list(mu = mu, sigma = sigma))

一旦指定的函数被编译，编译器就会抛出以下错误

Error in fitdist(data, "ZIP", start = list(mu = mu, sigma = sigma)) : 
  the function mle failed to estimate the parameters, 
                with the error code 100

很明显mu和sigma的起始值初始化有问题。我不确定在什么基础上初始化起始值。
任何帮助表示赞赏。

Answer 1

您可以使用VGAM::*zipois() 代替gamlss.dist::*ZIP()。起始参数有点不同，见?dzipois，不一定是你输入的平均值。

library('fitdistrplus')
library('VGAM')  
fitdist(x, 'zipois', start=list(lambda=1, pstr0=.1))
# $start.arg
# $start.arg$lambda
# [1] 1
# 
# $start.arg$pstr0
# [1] 0.1
# 
# 
# $fix.arg
# NULL
# 
# Fitting of the distribution ' zipois ' by maximum likelihood 
# Parameters:
#   estimate Std. Error
# lambda 12.2009631 0.23823650
# pstr0   0.1187056 0.02069464
# Warning messages:
#   1: In fitdist(x, "zipois", start = list(lambda = 1, pstr0 = 0.1)) :
#   The dzipois function should return a zero-length vector when input has length zero
# 2: In fitdist(x, "zipois", start = list(lambda = 1, pstr0 = 0.1)) :
#   The pzipois function should return a zero-length vector when input has length zero

不过，我不确定这个警告。

您可以使用不同的向量x1（如下）来比较它，gamlss.dist 不会失败。

---

数据：

x <- c(0, 1, 0, 11, 2, 0, 3, 0, 0, 2, 1, 3, 1, 0, 1, 0, 0, 0, 2, 3, 
0, 0, 0, 8, 1, 1, 1, 0, 1, 1, 2, 7, 0, 0, 0, 5, 2, 3, 6, 1, 1, 
5, 2, 9, 0, 0, 1, 21, 16, 2, 9, 6, 25, 2, 1, 12, 16, 14, 15, 
15, 6, 1, 12, 12, 13, 5, 5, 6, 4, 7, 11, 8, 4, 5, 8, 3, 8, 4, 
7, 4, 7, 2, 5, 6, 4, 5, 1, 0, 8, 5, 6, 8, 9, 8, 9, 7, 7, 9, 8, 
9, 4, 4, 7, 13, 9, 13, 12, 10, 9, 8, 7, 11, 5, 5, 0, 1, 33, 4, 
22, 19, 22, 9, 5, 4, 17, 7, 7, 4, 5, 3, 0, 0, 9, 3, 0, 0, 36, 
40, 5, 4, 0, 11, 0, 7, 5, 25, 39, 26, 4, 20, 12, 4, 17, 3, 22, 
12, 14, 8, 9, 11, 7, 11, 10, 9, 16, 6, 24, 8, 5, 6, 14, 3, 9, 
4, 1, 20, 0, 1, 7, 9, 0, 12, 2, 29, 56, 16, 8, 28, 0, 19, 25, 
35, 87, 56, 66, 60, 58, 14, 10, 12, 13, 13, 34, 26, 18, 13, 22, 
13, 12, 15, 41, 11, 11, 11, 5, 6, 7, 8, 8, 17, 16, 12, 21, 38, 
34, 10, 77, 41, 7, 12, 1, 16, 20, 8, 5, 2, 20, 7, 16, 12, 6, 
10, 31, 12)

x1 <- c(0, 63, 1, 4, 1, 44, 2, 2, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 3, 
0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
6, 1, 11, 1, 1, 0, 0, 0, 2)