pert distribution

[mathieu nacher]

hello i would like to know how to generate a PERT distribution from a low, high, and mean value say for a prevalence.
can anyone help?
thank you
mat

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

Also, assume we are not from your area of study. Do write out any acronyms and explain what you want in general statistical terms.

I don't know what you mean by PERT distribution - is this associated with a PERT chart? There are beta-PRET distribution estimators on line - while not written for Stata, they don't look that hard to program.

[William Lisowski]

Adding to Phil's advice, is it the case that the PERT distribution to which you refer is the one described in Wikipedia at https://en.wikipedia.org/wiki/PERT_distribution ?

Then, if so, what do you mean by "generate a PERT distribution"?

• generate a random variable chosen from the PERT distribution with the parameters specified?
• calculate the density function for the PERT distribution with the parameters specified?
• calculate the cumulative distribution function for the PERT distribution with the parameters specified?
• estimate the parameters of a PERT distribution from observed data?

My reading of the Wikipedia articles on the PERT distribution and Beta distribution suggests that the PERT distribution can be transformed into a four-parameter Beta distribution, which can in turn be transformed into a two-parameter Beta distribution.That's probably the route I would take if what is wanted is the density or distribution function: express the PERT distribution in terms of a two-parameter Beta distribution, and then use the existing tools for calculating density and distribution functions for the Beta distribution.

[mathieu nacher]

Hello, sorry for the imprecision. yes i was refering to the wikipedia definistion you cited. And i would be interested in generating a random variable from the specified parameters.
thanks for your help

[William Lisowski]

Do you speak SAS at all? The link below discusses generating random numbers from a PERT distribution with a specified minimum, mode, and maximum.

https://blogs.sas.com/content/iml/20...tribution.html

As I suspected, the procedure is to transform the PERT parameters into the parameters for a standard Beta distribution, generate a random numbers from that distribution, and then translate those to the desired PERT distribution.

In Stata, the rbeta() function generates random numbers from a Beta distribution with specified parameters.