FAQ/gamma - CBU statistics Wiki

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How do I produce random variables which follow a negatively skewed distribution?

Most distributions such as the exponential and log-Normal distributions are positively skewed with the mode of the distribution occurring for lower values.

The Weibull distribution is negatively skewed and may be generated using random variables which are uniform on the interval (0,1).

The below produces an open ended negatively skewed weibull distribution with parameters, 2 and 20. It has a median of

$$2text{-0.05}ln(2)text{0.05}$$ = 0.95.

which is of form

$$Atext{-1/B}ln(2)text{1/B}$$

where A and B are the two parameters of the Weibull distribution. (See here for formulae).

compute alpha=2.
compute beta=20.

compute rvw=((-1/alpha)*(ln(1-rv.uniform(0,1))))**(1/beta).
compute med=((alpha)**(-1/beta))*(ln(2)**(1/beta)).
exe.