R中已知分布的抽样

Question

到目前为止，我已经确定了适当的发行版本(使用格列奈特和“碎牛肉”数据)：

> library(fitdistrplus)
> data("groundbeef")
> str(groundbeef)
'data.frame':   254 obs. of  1 variable:
 $ serving: num  30 10 20 24 20 24 40 20 50 30 ...
> descdist(groundbeef$serving, boot = 1000)
summary statistics
------
min:  10   max:  200 
median:  79 
mean:  73.64567 
estimated sd:  35.88487 
estimated skewness:  0.7352745 
estimated kurtosis:  3.551384 
> fw<-fitdist(groundbeef$serving, "weibull")
> fg<-fitdist(groundbeef$serving, "gamma")
> fln<-fitdist(groundbeef$serving, "lnorm")
> gofstat(list(fw, fg, fln), fitnames = c("weibull", "gamma", "lnorm"))
Goodness-of-fit statistics
                               weibull     gamma     lnorm
Kolmogorov-Smirnov statistic 0.1396646 0.1281246 0.1493090
Cramer-von Mises statistic   0.6840994 0.6934112 0.8277358
Anderson-Darling statistic   3.5736460 3.5660192 4.5436542

Goodness-of-fit criteria
                                weibull    gamma    lnorm
Aikake's Information Criterion 2514.449 2511.250 2526.639
Bayesian Information Criterion 2521.524 2518.325 2533.713

在此基础上，我可以选择伽马分布来描述数据。我现在要做的是看看数据的不同样本大小是如何影响gof的。例如，当前的gof是基于254个观测结果的--如果我只使用其中50个观测值的随机样本，那么gof会发生什么变化？在某个时刻，必须有一个γ不再合适的阈值(即，1的样本不能最好地用这些分布来描述)。我看过这，这或多或少是我希望做的，除了只有一个数据组(也就是‘磨牛肉$serving’)，我不感兴趣的计算能力，而是跟踪p值的变化，因为我使用不同的样本大小。

Answer 1

随机样本大小N 1000倍于原始数据集，测试每个随机样本的拟合优度，查看1000 gof测试的平均值p值。

df <- groundbeef

for (i in 1:1000) {

    temp2 <- sample(df$serving, size=50, replace=FALSE)
    #descdist(temp2, boot = 1000)
    fw <- fitdist(temp2, "weibull")
    fg <- fitdist(temp2, "gamma")
    fln <- fitdist(temp2, "lnorm")
    gof <- gofstat(list(fw, fg, fln), fitnames = c("weibull", "gamma", "lnorm"))$chisqpvalue

    if(i == 1) { results <- gof }
    if(i > 1) { results <- rbind(results, gof) }

}

row.names(results) <- c(1:nrow(results))
results <- as.data.frame(results)
summary(results)

 weibull              gamma               lnorm         
Min.   :0.0000000   Min.   :0.0000000   Min.   :0.000000  
1st Qu.:0.0000001   1st Qu.:0.0000001   1st Qu.:0.000000  
Median :0.0009940   Median :0.0035025   Median :0.003264  
Mean   :0.0380086   Mean   :0.0519209   Mean   :0.058692  
3rd Qu.:0.0383365   3rd Qu.:0.0578076   3rd Qu.:0.056701  
Max.   :0.7309149   Max.   :0.8963196   Max.   :0.855437