# Re: st: RE: Cumulative Distribution Function

 From Alison Wong To statalist@hsphsun2.harvard.edu Subject Re: st: RE: Cumulative Distribution Function Date Fri, 13 Sep 2002 11:33:50 -0600

Hi:
Here is more information about my problem. In a block sense, I am trying to calculate the Inverse Mill Ratio (IMR) to be use to calculate some form of generalized residual. I read this method from Francis Vella's article:

"A Simple Estimator for Simultaneous Models with Censored Regressors", International Economic Review, Volume 34, Issue 2 (May, 1993), 441-457.
In his article he suggested if you have a censored endogenous variable in a simultaneous equation system, than you could use a two step procedure (similar to the one Heckman presents) to get consistent estimates. The first step is to regress the reduced form of the censored endogenous variable using tobit. By that you should get estimates of coefficients (beta) and standard errors (sigma), then you could use these estimates to calculate the generalized residuals. The problem is in his generalized residual equation, he has the cumulative distribution function (cdf) and probability density function (pdf) in it and presented in the form similar to the Inverse Mill Ratio. This is the part that I can't figure out how to calculate, because I can't find anything in Stata that would calculate the Inverse Mill Ratio, of course, it calculate the IMR in the two step Heckman command but I don't want to use the Heckman command, so is there any other ways to obtain the IMR?

I hope I provide enough information this time. If anyone is interested in this paper pls. let me know and I could send you a copy of this paper. I would really appreciate if anyone who had read this article to tell me how to calculate the generalized residuals using Stata.
Thank you!

Alison

FEIVESON, ALAN H. (AL) (JSC-SD) (NASA) wrote:

Alison -
I'm afraid your question is not specific enough. What model are you running
to get estimates of your coefficients? What random variable do you want to
get the cdf and/or pdf for? What distribution does it have under the assumed
model? Do you want to evaluate this cdf/pdf as a function prescribed by your
model over a range of values, or do you want to compute an empirical cdf or
pdf from data?

Al Feiveson

-----Original Message-----
From: Alison Wong [mailto:aliwong@ucalgary.ca]
Sent: Thursday, September 12, 2002 12:01 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: Cumulative Distribution Function

Hi:

I have a problem of getting the cumulative distribution function (cdf) and probability density function (pdf). In particular I need to get the cdf and pdf evaluated at the estimated coefficients (beta) and standard errors (sigma). I realize there are the "cumul" & "kdensity" command in stata, but those only allows a single variable, but I have more than one variable.

Does anyone have a better idea of how to get cdf or pdf?

Thanks.

Alison Wong

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