Some other graphical methods, maybe more helpful than the simple histogram. I will illustrate with graphics produced with the help of R. First a plot visualizing the data together with some possible theoretical distributions in a skewness-kurtosis space:
library(fitdistrplus) # on CRAN
dat <- read.table("gamma2.test", header=FALSE) # poster's data
gamma2 <- dat$V1
descdist(gamma2, boot=1000) # Cullen and Frey-plot
The orange values around the blue (data) point are based on bootstrapping. We can see that kurtosis are somewhat larger than what can be accommodated by gamma, weibull or lognormal distributions, while skewness is smaller.
We can make some more detailed comparisons:
gammafit <- fitdistrplus::fitdist(gamma2, "gamma")
weibullfit <- fitdistrplus::fitdist(gamma2, "weibull")
lnormfit <- fitdistrplus::fitdist(gamma2, "lnorm") # not supported?
library(flexsurv) # on CRAN
gengammafit <- fitdistrplus::fitdist(gamma2, "gengamma",
then we can compare the fits with qqplots:
qqcomp(list(gammafit, weibullfit, lnormfit, gengammafit),
legendtext=c("gamma", "lnorm", "weibull", "gengamma") )
and we can see that indeed the generalized gamma seems to fit better, especially in the left (lower) tail. None of the distributions fit very well in the right (upper) tail, but the generalized gamma is best. For general help on qqplots, see How to interpret a QQ plot .
Another way of doing the comparison is a relative density plot, let us use the best fitting generalized gamma distribution as reference distribution. Then if the data exactly follows the reference distribution, the plot will be a uniform density. See What are good data visualization techniques to compare distributions? for details.
library(reldist) # on CRAN
N <- length(gamma2)
q_rel <- qgengamma(ppoints(N), mu=gengammafit$estimate["mu"],
reldist(gamma2, q_rel, main="Relative distribution comp to generalized gamma")
(please note the vertical (density) scale, all relative density values are quite close to 1, so the theoretical reference model is quite good)