从rpois生成正实数()

Question

我正在尝试使用rpois().创建泊松模拟.我有两个小数位利率的分布,我想知道它们是否具有泊松而不是正态分布.

该rpois()函数返回正整数.我希望它返回两个小数位的正数而不是.我尝试了以下内容

set.seed(123)
trialA <- rpois(1000, 13.67) # generate 1000 numbers
mean(trialA)
13.22 # Great! Close enough to 13.67
var(trialA)
13.24 # terrific! mean and variance should be the same
head(trialA, 4) 
6 7 8 14 # Oh no!! I want numbers with two decimals places...??????

# Here is my solution...but it has a problem

# 1) Scale the initial distribution by multiplying lambda by 100

trialB <- rpois(1000, 13.67 * 100)

# 2) Then, divide the result by 100 so I get a fractional component
trialB <- trialB / 100
head(trialB, 4) # check results
13.56 13.62 13.26 13.44 # terrific !

# check summary results
mean(trialB)
13.67059  # as expected..great!
var(trialB)
0.153057 # oh no!! I want it to be close to: mean(trialB) = 13.67059

如何使用rpois()生成具有泊松分布的正两位小数.

我知道泊松分布用于计数,而计数是正整数,但我也相信泊松分布可用于模拟速率.这些速率可能只是正整数除以标量.

Answer 1

如果缩放泊松分布以改变其均值,则结果不再是泊松,并且均值和方差不再相等 - 如果您将均值缩放一个因子s,则方差会更改一个因子s^2.

您可能想要使用Gamma分布.Gamma的平均值shape*scale和方差是shape*scale^2,所以你必须scale=1用来得到具有相等均值和方差的实数,正数:

set.seed(1001)
r <- rgamma(1e5,shape=13.67,scale=1)
mean(r) ## 13.67375
var(r)  ## 13.6694

您可以舍入到小数点后两位而不会更改均值和方差:

r2 <- round(r,2)
mean(r2) ## 13.67376
var(r2)  ## 13.66938

与泊松分布比较:

par(las=1,bty="l")
curve(dgamma(x,shape=13.67,scale=1),from=0,to=30,
      ylab="Probability or prob. density")
points(0:30,dpois(0:30,13.67),type="h",lwd=2)