*! version 1.0 28apr2022

Title

pdfplot -- Plot a Distribution's Probability Density Function

Syntax

pdfplot
dist_name, params(numlist) [range()]

Supported distributions come from the Skewed Generalized t and Generlized Beta of the Second Kind families of distributions, namely:

Distribution dist_name params

Normal normal mu, sigma
Skewed Normal snormal mu, sigma, lambda
Laplace laplace mu, sigma
Skewed Laplace slaplace mu, sigma, lambda
Generalized Error ged mu, sigma, p
Skewed Generalized Error sged mu, sigma, p, lambda
t t mu, sigma, q
Generalized t gt mu, sigma, p, q
Skewed t st mu, sigma, q, lambda
Skewed Generalized t sgt mu, sigma, p, q, lambda
Lognormal lnormal mu, sigma
Weibull weibull a, b
Gamma gamma b, p
Generalized Gamma ggamma a, b, p
Burr type 3 br3 a, b, p
Burr type 12 br12 a, b, q
Generalized Beta of the Second Kind gb2 a, b, p, q

Description

pdfplot is a tool to efficiently plot the PDF of one of the above distributions with chosen parameter values. It uses twoway_function to do so. pdfplot was originally developed as a companion to gintreg, which performs maxiumum likelihood estimation on any of the same set of accepted distributions and is compatible with numerous forms of data, including point, interval, truncated, censored and grouped data.

Examples

Plotting a Standard Normal PDF

. pdfplot normal, params(0 1) range(-4 4)

Plotting a Generalized Gamma PDF with chosen parameters

. pdfplot ggamma, params(10 20 .3) range(0 30)

Plotting a Skewed Generalized t PDF with an adjusted lambda after estimating with gintreg

. webuse intregxmpl

. gintreg wage1 wage2, dist(sgt)

. pdfplot sgt, params(7.423 1.743 1.846 1) range(0 50)

Author

Authored by Jacob Triplett at Brigham Young University while working with James B. McDonald to modify the gintreg program. For support contact Jacob at "jacobwtriplett@icloud.com".

References

McDonald, J. B., Some Generalized Functions for the Size Distribution of Income, Econometrica, 52 (1984), 647-663.

McDonald, J. B. and R Michefelder, Partially Adaptive and Robust Estimation of Asset Models: Accommodating Skewness in Returns, Journal of Mathematical Finance, 7 (2017), 219-237.

Theodosssiou, P., Financial Data and the Skewed Generalized t Distribution, Management Science, December 1988, 44(12), 1650-1661.

Skewed Generalized t Distribution, Wikipedia, "https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution".

Generalized Beta of the Second Kind Distribution, Wikipedia, "https://en.wikipedia.org/wiki/Generalized_beta_distribution#Generalized_beta_of_the_second_kind_(GB2)".