Diff for "FAQ/gamma" - CBU statistics Wiki
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Differences between revisions 19 and 25 (spanning 6 versions)
 ⇤ ← Revision 19 as of 2008-02-13 11:14:12 → Size: 758 Editor: PeterWatson Comment: ← Revision 25 as of 2013-03-08 10:17:36 → ⇥ Size: 981 Editor: localhost Comment: converted to 1.6 markup Deletions are marked like this. Additions are marked like this. Line 5: 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)] 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 13: Line 13: (See [http://www.weibull.com/AccelTestWeb/weibull_distribution.htm here for formulae).] which is of form\$\$A^text{-1/B}ln(2)^text{1/B}\$\$where A and B are the two parameters of the Weibull distribution.(See [[http://www.weibull.com/AccelTestWeb/weibull_distribution.htm|here for formulae).]] Line 16: Line 21: compute wrv= (-(1/2)*(ln(1-rv.uniform(0,1))))**(0.05). 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)).

# 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.```

None: FAQ/gamma (last edited 2013-03-08 10:17:36 by localhost)