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From |
"Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov> |

To |
"statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Evaluate cdf and pdf of mixture of normals |

Date |
Fri, 2 Sep 2011 08:03:25 -0500 |

Fernando - For any mixture, the CDF (and also the PDF) is just the weighted sum of its components. So if you are asking how to do this in Stata, it depends on how those component CDFs, etc are stored in your application. Are they Stata "variables" evaluated at each observation of the data set? Or what? Al Feiveson -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Fernando Luco Sent: Thursday, September 01, 2011 2:58 PM To: statalist@hsphsun2.harvard.edu Subject: st: Evaluate cdf and pdf of mixture of normals Dear statalisters, I'm trying to compute the cdf and pdf of a mixture of normals but the specifics of my problem are doing this quite difficult, so any ideas would be really appreciated. My data, and what I want to do is as follows. I have i people that may or may not be present at t situations. Each person has two variables associated, y(it) and x(it). I assume that the distribution of y(it) satisfies y(it)=x(it)+e(it) where the distribution of e(it) is a mixture of normals. Let's assume that is only a mixture of two normals to make it easy and that they have means mu1 and mu2 and std. dev sigma1 and sigma2, and are independent. I have the means, variances and mixing probabilities of the distribution of e(it). So, my data is t, i, y(it) and x(it). I have heterogeneity between people so the distributions of y(i) differ among people, in particular, the mean changes. So, for example, when considering the cdf of person 1 the mean should be x11 plus the two means of the normal distributions (I guess that they enter weighted by the mixing probabilities), for situation 1, but for situation 2 then the mean should be x12 plus the weighted means. For person 2 the mean would be x21 plus the weighted means of the normals for situation one, and x22 for situation two, etc. The variance is common. I want to evaluate the cdf and the pdf at y(it). Finally, not every people are present in every t. So, when person i is not present then the cdf and pdf should be empty. Does anybody know how I can compute this in Stata? Thanks in advanced, Fernando * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Evaluate cdf and pdf of mixture of normals***From:*Fernando Luco <flucoestatalist@gmail.com>

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