gecrooks / fieldguide

Field Guide to Continuous Probability Distributions by Gavin E. Crooks

Field Guide to Continuous Probability Distributions

Gavin E. Crooks

A survey of probability distributions used to describe a single, continuous, univariate random variable.

PDF: https://threeplusone.com/fieldguide

Source Code: https://github.com/gecrooks/fieldguide

Amazon: https://www.amazon.com/dp/1733938109/

Compile: latexmk -xelatex FieldGuide.tex

Citation: @book{FieldGuide, Author = {Gavin E. Crooks}, Edition = {1.0}, Note = {\url{https://threeplusone.com/fieldguide}}, Publisher = {BITS}, Title = {Field guide to continuous probability distributions}, Year = {2019}}

fieldguide's Issues

GenBetaPrime

p. 124 it says:
Dagum(gamma, beta) = GenBetaPrime(a,s,1,gamma,-beta)
But Dagum only depends on two parameters (gamma,beta), not also on (a,s).

LogLogistic(a,s,beta) = GenBetaPrime(0,s,1,1,beta)
But LogLogistic only depends on 3 parameters (a,s,beta), but GenBetaPrime is missing a.

Also, the Kumaraswamy distribution is usually defined to be a two parameter family of distributions. But on p117 it depends on (a,s,gamma,beta)

Table 17.1 Special cases of generalized beta

Since Pert is a special case of Beta, and Beta is a special case of Generalized Beta, then shouldn't Pert also be in Table 17.1?

Pareto equation wrong

• the pdf for the Pareto distribution is parametrized with \gamma yet the equation references negative \beta

Tracy-Widom distribution

and beta-Tracy-Widom distributions.

Kudos: Aaron Dinner for pointing out the omission.

Review Distributions.jl

Review the distributions implemented (or planned to be implemented) in Distributions.jl (https://github.com/JuliaStats/Distributions.jl), and look for distributions missing from the field guide. See issue #1

JuliaStats/Distributions.jl#124

https://github.com/taqtiqa-mark/Distributions.jl/blob/563ea34b42e94277baa918ccc9610a3d5b6b838d/docs/src/univariate-list.md

Generalized Lambda Distribution?

Unless I missed it, I don't think your guide has the Generalized Lambda Distribution (GLD).
For examples: https://arxiv.org/pdf/1907.06336.pdf
This four-parameter distribution is also pretty flexible.

Skewed Generalized T Distribution

Unless I missed it, I don't think your guide has the Skewed Generalized T Distribution, a 5-parameter distribution that nests:
skewed generalized error distribution,
the generalized t distribution,
skewed t,
skewed Laplace distribution,
generalized error distribution,
skewed normal distribution,
student t distribution,
skewed Cauchy distribution,
Laplace distribution,
uniform distribution,
normal distribution,
Cauchy distribution

https://cran.r-project.org/web/packages/sgt/vignettes/sgt.pdf

Wrong sign for generalized Gumbel

I believe that the sign is incorrect in the parameterisation linking the generalized Gumbel distribution to its parent gamma-exponential distribution (8.4). Should it not be: GenGumbel(x; u, λ, n) = GammaExp(x; u + λ \ln n, λ, ν)? Version 1.0.0 of the field guide has a minus sign.