Solved – What distribution would lead to this highly peaked and skewed density plot

distributionsr

The density of my data set was plotted in R as follows.

enter image description here

What kind of distribution would fit this data?

As I am not experienced to tell by visualization, I can only guess it is not normally distributed. I shall test it with R: some guidance as a starting point is highly desirable.

Best Answer

It looks rather like an exponential distribution (assuming that the bit below 0 is an artifact of smoothing in the density estimation).

I would look at a qqplot. In R, if x contains your data:

n <- length(x)
qqplot(x, qexp( (1:n - 0.5)/n ) )

Note that in the use of density() for the non-negative case, it is best to use from=0 since you know the density is 0 below 0.

plot(density(x, from=0))

I think also that, if $X$ follows an exponential distribution, then $e^{-X/\mu_X}$ should follow a uniform distribution, so the following could be a reasonable diagnostic:

hist(exp(-x/mean(x)), breaks=2*sqrt(length(x)))
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