Given a set of random numbers drawn from a continuous univariate distribution, find the distribution

Question

Given a set of real numbers drawn from a unknown continuous univariate distribution (let\'s say is is one of beta, Cauchy, chi-square, exponential, F, gamma, Laplace, log-no

Answer 1

My first approach would be to generate qq plots of the given data against the possible distributions.

x <- c(15.771062,14.741310,9.081269,11.276436,11.534672,17.980860,13.550017,13.853336,11.262280,11.049087,14.752701,4.481159,11.680758,11.451909,10.001488,11.106817,7.999088,10.591574,8.141551,12.401899,11.215275,13.358770,8.388508,11.875838,3.137448,8.675275,17.381322,12.362328,10.987731,7.600881,14.360674,5.443649,16.024247,11.247233,9.549301,9.709091,13.642511,10.892652,11.760685,11.717966,11.373979,10.543105,10.230631,9.918293,10.565087,8.891209,10.021141,9.152660,10.384917,8.739189,5.554605,8.575793,12.016232,10.862214,4.938752,14.046626,5.279255,11.907347,8.621476,7.933702,10.799049,8.567466,9.914821,7.483575,11.098477,8.033768,10.954300,8.031797,14.288100,9.813787,5.883826,7.829455,9.462013,9.176897,10.153627,4.922607,6.818439,9.480758,8.166601,12.017158,13.279630,14.464876,13.319124,12.331335,3.194438,9.866487,11.337083,8.958164,8.241395,4.289313,5.508243,4.737891,7.577698,9.626720,16.558392,10.309173,11.740863,8.761573,7.099866,10.032640)
> qqnorm(x)

For more info see link

Another possibility is based on the fitdistr function in the MASS package. Here is the different distributions ordered by their log-likelihood

> library(MASS)
> fitdistr(x, 't')$loglik
[1] -252.2659
Warning message:
In log(s) : NaNs produced
> fitdistr(x, 'normal')$loglik
[1] -252.2968
> fitdistr(x, 'logistic')$loglik
[1] -252.2996
> fitdistr(x, 'weibull')$loglik
[1] -252.3507
> fitdistr(x, 'gamma')$loglik
[1] -255.9099
> fitdistr(x, 'lognormal')$loglik
[1] -260.6328
> fitdistr(x, 'exponential')$loglik
[1] -331.8191
Warning messages:
1: In dgamma(x, shape, scale, log) : NaNs produced
2: In dgamma(x, shape, scale, log) : NaNs produced