Diff for "FAQ/gamma" - CBU statistics Wiki
location: Diff for "FAQ/gamma"
Differences between revisions 3 and 4
Revision 3 as of 2008-02-12 17:24:10
Size: 859
Editor: PeterWatson
Comment:
Revision 4 as of 2008-02-12 17:30:27
Size: 1095
Editor: PeterWatson
Comment:
Deletions are marked like this. Additions are marked like this.
Line 3: Line 3:
Most distributions such as the exponential and log-Normal distributions are positive skewed with the mode of the distribution occurring for lower values.
Line 4: Line 5:
Most distributions such as the exponential and log-Normal distributions are positive skewed with the model of the distribution for lower values. The Gamma distribution[http://www.aiaccess.net/English/Glossaries/GlosMod/e_gm_gamma_distri.htm
may be produced by summing exponential distributions.] There are two parameters, n and $$\lambda$$. n is the number of summed exponentials and $$\lambda$$ is the exponential rate. When $$\lambda$$ is very small compared to n a negative skewed version of the gamma distribution results with no upper limit.
Line 6: Line 8:

[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.

The below produces negatively skewed data with no upper bound.
The below produces two exponential random variables (n=2) with a very small $$\lambda$$ (=1/10000) in SPSS. One simulated data set produced using this macro had a skew of -1.03.

How do I produce random variables which follow a negative skew distribution?

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

The Gamma distribution[http://www.aiaccess.net/English/Glossaries/GlosMod/e_gm_gamma_distri.htm may be produced by summing exponential distributions.] There are two parameters, n and $$\lambda$$. n is the number of summed exponentials and $$\lambda$$ is the exponential rate. When $$\lambda$$ is very small compared to n a negative skewed version of the gamma distribution results with no upper limit.

The below produces two exponential random variables (n=2) with a very small $$\lambda$$ (=1/10000) in SPSS. One simulated data set produced using this macro had a skew of -1.03.

define !gamma ( !pos !tokens(1)
                /!pos !tokens(1)).
!do !i=!1 !to !2 !by 1.
compute !concat(a,!i)=-(10000)*ln(rv.uniform(0,1)*10000).
!doend.
!enddefine.

!gamma 1 2.
exe.

compute sum=0.
exe.


compute sum=-(a1+a2).
exe.

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