topic Re: How to incorporate shape, scale and location parameters using RAND("LOGNORMAL") in Statistical Procedures

How to incorporate shape, scale and location parameters using RAND("LOGNORMAL")

jonesk48 — Tue, 17 May 2016 20:49:56 GMT

Hello All,

I am starting to do more simulations and have a general question regarding simulating a lognormal distribution. I have existing data that looks like the following (I've fitted a lognormal curve to the data). I would like to simulate more data using the MLE estimated shape, scale and location parameters for the exisiting data. I noticed the RAND function does not support location, shape or scale for the lognormal distribution. How can I incorporate these parameters so that I can simulate data to look like my original data? I thought I could do Y = location parameter + scale parameter*X, where X =RAND("LOGNORMAL"). Am I on the right track here? Any help appreciated!!!

Re: How to incorporate shape, scale and location parameters using RAND("LOGNORMAL")

jonesk48 — Tue, 17 May 2016 20:55:54 GMT

Just for clarity, the embedded picture is from my acutal data. I would like to simulate more data that looks like this.

Re: How to incorporate shape, scale and location parameters using RAND("LOGNORMAL")

ballardw — Tue, 17 May 2016 21:13:22 GMT

Look at the PDF('LOGNORMAL') function

Re: How to incorporate shape, scale and location parameters using RAND("LOGNORMAL")

jonesk48 — Tue, 17 May 2016 21:19:55 GMT

Yes I will, thank you! I didn't think about using the pdf function.

Re: How to incorporate shape, scale and location parameters using RAND("LOGNORMAL")

Rick_SAS — Wed, 18 May 2016 01:08:01 GMT

Chapter 7 of Wicklin (2013) Simulating Data with SAS has a section on "Adding Location and Scale Parameters" (p. 107-109).

For the lognormal function it says:

The RAND("Normal", mu, sigma) function generates X ~ N(mu, sigma). The random variable Y = exp(X) is

lognormally distributed with parameters mu and sigma..... Notice that the location and scale parameters are added before the

exponential transformation is applied.

You can add a threshold parameter by generating theta+Y.

For an example in teh DATA step, see "Simulate lognormal data with specified mean and variance."

Re: How to incorporate shape, scale and location parameters using RAND("LOGNORMAL")

Ksharp — Wed, 18 May 2016 01:13:11 GMT

Rick's blog might give you some help.

http://blogs.sas.com/content/iml/2014/06/04/simulate-lognormal-data-with-specified-mean-and-variance.html

Re: How to incorporate shape, scale and location parameters using RAND("LOGNORMAL")

jonesk48 — Wed, 18 May 2016 12:42:28 GMT

Hi Rick,

Thank you for the feedback! I understand now, and the link you provided with the example helps greatly.

Re: How to incorporate shape, scale and location parameters using RAND("LOGNORMAL")

jonesk48 — Wed, 18 May 2016 12:43:34 GMT

Thank you! This link is very helpful, Rick also referred to the same content on his blog. I appreciate your feedback!