<?xml version="1.0" encoding="utf-8"?><!DOCTYPE article  PUBLIC '-//OASIS//DTD DocBook XML V4.4//EN'  'http://www.docbook.org/xml/4.4/docbookx.dtd'><article><articleinfo><title>FAQ/gamma</title><revhistory><revision><revnumber>25</revnumber><date>2013-03-08 10:17:36</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>24</revnumber><date>2008-02-13 14:51:32</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>23</revnumber><date>2008-02-13 14:51:08</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>22</revnumber><date>2008-02-13 12:35:59</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>21</revnumber><date>2008-02-13 12:16:55</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>20</revnumber><date>2008-02-13 11:14:21</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>19</revnumber><date>2008-02-13 11:14:12</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>18</revnumber><date>2008-02-13 10:53:38</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>17</revnumber><date>2008-02-13 10:53:14</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>16</revnumber><date>2008-02-13 10:52:11</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>15</revnumber><date>2008-02-13 10:51:59</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>14</revnumber><date>2008-02-13 10:49:57</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>13</revnumber><date>2008-02-13 10:49:16</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>12</revnumber><date>2008-02-13 10:48:16</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>11</revnumber><date>2008-02-13 10:47:46</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>10</revnumber><date>2008-02-13 10:36:35</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>9</revnumber><date>2008-02-12 17:32:51</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>8</revnumber><date>2008-02-12 17:32:11</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>7</revnumber><date>2008-02-12 17:31:16</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>6</revnumber><date>2008-02-12 17:31:04</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2008-02-12 17:30:49</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2008-02-12 17:30:27</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2008-02-12 17:24:10</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2008-02-12 16:41:35</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2008-02-12 16:40:26</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>How do I produce random variables which follow a negatively skewed distribution?</title><para>Most distributions such as the exponential and log-Normal distributions are positively skewed with the mode of the distribution occurring for lower values. </para><para>The Weibull distribution is negatively skewed and may be generated <ulink url="http://www.taygeta.com/random/weibull.xml">using random variables which are uniform on the interval (0,1).</ulink> </para><para>The below produces an open ended negatively skewed weibull distribution with parameters, 2 and 20. It has a median of </para><para>$$2<superscript>text{-0.05}ln(2)</superscript>text{0.05}$$ = 0.95. </para><para>which is of form </para><para>$$A<superscript>text{-1/B}ln(2)</superscript>text{1/B}$$ </para><para>where A and B are the two parameters of the Weibull distribution. (See <ulink url="http://www.weibull.com/AccelTestWeb/weibull_distribution.htm">here for formulae).</ulink> </para><screen><![CDATA[compute alpha=2.
compute beta=20.
]]><![CDATA[
compute rvw=((-1/alpha)*(ln(1-rv.uniform(0,1))))**(1/beta).
compute med=((alpha)**(-1/beta))*(ln(2)**(1/beta)).
exe.]]></screen></section></article>