如何估算伽玛距离的形状和比例.具有特定的均值和95％的分位数? [英] How can I estimate the shape and scale of a gamma dist. with a particular mean and a 95% quantile?

问题描述

在给定特定的平均值(或中位数)和特定的分位数(95％的分位数)的情况下，R中是否有任何方法可以计算伽玛分布的比例和形状?

Is there any way, in R, to calculate the scale and shape of a gamma distribution, given a particular value of mean (or median) and a particular quantile (the 95% quantile)?

例如，我有一个平均值= 130

和 95％的分位数= 300

分布的偏移量为 80

是否有任何方法可以获取满足这些条件的伽玛标尺和形状?

is there any way to obtain the scale and shape of a gamma that meet these criteria?

推荐答案

这是一种方法:

myfun <- function(shape) {
    scale <- 130/shape
    pgamma(300, shape, scale=scale) - 0.95
}

tmp <- uniroot( myfun, lower=2, upper=10 )

myshape <- tmp$root
myscale <- 130/tmp$root

qgamma(0.95, shape=myshape, scale=myscale)
integrate( function(x) x*dgamma(x,shape=myshape,scale=myscale), 
    lower=0, upper=Inf )

我不确定您所说的80偏移量是什么意思，如果那恰好是伽马变为非零的位置，则从130和300中减去80并执行与上述相同的操作.

I am not sure what you mean by offset of 80, if that is just where the gamma becomes non-zero then subtract 80 from 130 and 300 and do the same as above.

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