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 ⇤ ← Revision 1 as of 2008-02-12 16:40:26 → Size: 448 Editor: PeterWatson Comment: ← Revision 20 as of 2008-02-13 11:14:21 → ⇥ Size: 759 Editor: PeterWatson Comment: Deletions are marked like this. Additions are marked like this. Line 1: Line 1: = 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. Line 2: Line 5: = The Weibull distribution is negatively skewed and may be generated [http://www.taygeta.com/random/weibull.xml using random variables which are uniform on the interval (0,1).] Line 4: Line 7: Most distributions such as the exponential and log-Normal distributions are positive skewed with the model of the distribution for lower values. The below produces an open ended negatively skewed weibull distribution with parameters, 2 and 20. It has a median of Line 7: Line 10: [http://www.uib.no/people/ngbnk/kurs/notes/node31.html The Gamma distribution] which has two parameters, $$\alpha$$ and $$\beta$$ may produce negative skew where the model occurs for higher values (values > 0) when $$/alpha$$ is a lot greater than $$\beta$$. It also has no maximum value. $$2^text{-0.05}ln(2)^text{0.05}$$= 0.95.(See [http://www.weibull.com/AccelTestWeb/weibull_distribution.htm here for formulae).]{{{compute wrv= (-(1/2)*(ln(1-rv.uniform(0,1))))**(0.05).exe.}}}

# 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 [http://www.taygeta.com/random/weibull.xml 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.

(See [http://www.weibull.com/AccelTestWeb/weibull_distribution.htm here for formulae).]

compute wrv= (-(1/2)*(ln(1-rv.uniform(0,1))))**(0.05).
exe.

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