1125
Comment:

600

Deletions are marked like this.  Additions are marked like this. 
Line 5:  Line 5: 
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 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 7:  Line 7: 
The below produces two exponential random variables (n=2) with a very small $$\lambda$$ (=1/10000) in SPSS and sums them. One resulting simulated data set produced using this macro had a skew of 1.03.  The below produces an open ended negatively skewed weibull distribution with parameters, 2 and 20. 
Line 10:  Line 10: 
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). 
compute wrv= ((1/2)*(ln(1rv.uniform(0,1))))**(0.05). 
How do I produce random variables which follow a negatively skewed distribution?
Most distributions such as the exponential and logNormal 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.
compute wrv= ((1/2)*(ln(1rv.uniform(0,1))))**(0.05). exe.