STAT 380 Lecture 26

Example: Half normal distribution: X has density

(Density of absolute value of N(0,1).)

Use . To find c maximize

Rewrite as

Maximum is at x=a giving

Choose a to minimize c (or ); get a=1 so

Algorithm is then: generate and then compute

Generate and if

accept Y otherwise try again.

To generate N(0,1): use a third U to pick a sign at random: negative if u < 1/2 otherwise positive.

Discrete Distributions

The inverse transformation method works for discrete distributions.

X has possible values with probabilities compute cumulative probabilities

with .

Generate Uniform(0,1).

Find k such that

Put .