哪种分布更适合数据？

Question

我fitdistr在R中用来选择最适合我数据的分布.

我尝试过Cauchy,Weibull,normal和Gamma分布.

对数似然值为:Cauchy为-329.8492,Gamma为-277.4931,正常为-327.7622,Weibull为-279.0352.

哪一个是最好的？具有最大值的那个(即Gamma)或具有最大abs的那个(即Cauchy)？

Answer 1

投票结束,但一个简单的测试将回答你的问题

set.seed(1)
# we know these data are normally distributed... 
dat <- rnorm(500,10,1)

# let's compute some fits...
require(MASS)
fits <- list(
 no = fitdistr(dat,"normal"),
 lo = fitdistr(dat,"logistic"),
 ca = fitdistr(dat,"cauchy"),
 we = fitdistr(dat, "weibull")
 )

# get the logliks for each model...
sapply(fits, function(i) i$loglik)

       no        lo        ca        we 
-718.3558 -722.1342 -806.2398 -741.2754

因此,最大值的loglik是指示最佳值的loglik.我们输入正态分布的数据,正常拟合的loglik是最大的.

您也可以从http://people.stern.nyu.edu/adamodar/pdfiles/papers/probabilistic.pdf找到此图片.