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From |
Reza C Daniels <[email protected]> |

To |
[email protected] |

Subject |
st: Clumsy solution: skewed distributions |

Date |
Thu, 29 Sep 2005 16:20:24 +0200 |

Hi,

I've come up with a fairly clumsy solution to the thread: "Generating skewed distributions on closed intervals" that we have been discussing today.

---

set obs 1000

gen u1=uniform()

gen b1=invnibeta(4,4,1,uniform()) /*symmetric*/

gen b2=invnibeta(4,2,1,uniform()) /*negative skew*/

gen b3=invnibeta(2,4,1,uniform()) /*positive skew*/

/* Apply following transformation to get range within desired interval [20,30] */

gen u2=20+(10*u1)

/* Repeat transformation above for b1-b3 */

---

A problem with this is that I get observations in the range (20,30) not [20,30]. I just can't seem to find a solution to explicitly stating the range of the beta distribution using -invnibeta-.

Any suggestions on improvements for the code below are of course welcomed.

Reza

Maarten Buis wrote:

`There are various skewed distributions to choose from: the lognormal, Chi square, F, gamma. These all have a range from 0 to positive infinity. A distribution that can be skewed, symmetric or flat depending on its parameters, and remains between a fixed range is the beta distribution. -----Original Message----- From: [email protected] [mailto:[email protected]]On Behalf Of Reza C Daniels Sent: donderdag 29 september 2005 13:29 To: [email protected] Subject: Re: st: RE: Generating skewed distributions on closed intervals Hi Maarten, My problem is exactly one of data coarsening, as explained by Heitjan and Rubin (JASA, 1991). The exception is that they applied this to heights and I'm wanting to apply it to age. I am also aware of the need to multiply impute. However, I wanted the uniform, normal and skewed distributions first before imputing, so that once I obtained the multiply imputed estimates, I would have something to compare them to. Reza Maarten Buis wrote:`

`Hi Reza, Will you be using this new age variable as a dependent/explained/y-variable or as an independent/explanatory/x-variable? If you are using age as an explained variable you will probably end up in survival analysis, and they have good techniques of dealing with discrete time, so I see no need to invent something new there. See: "An Introduction to Survival Analysis Using Stata" by Mario Cleves, William W. Gould, and Roberto Gutierrez available from Stata Press. If you will be using age as an explanatory variable than it is good to know that even very coarsely categorized variables often produce good estimates. If you still want to do something about the categorisation, than you would probably want to do some form of multiple imputation. The way to think about it is that there is one age distribution, which was chopped up in bits. You don't want to use different distributions for each age band, since than you would assume a very bumpy overall age distribution. So you would first estimate the parameters of this age distribution. Than if you wanted to draw an age for a person in category 20-30, you would draw from a value this distribution truncated between 20 and 30. You would create multiple datasets this way, estimate the regression or whatever other parameter of interest for each of these datasets, and the mean of these effects would be your estimate controlling for the categorisation of age. However, I repeat that this is probably more trouble that its worth. I'd like to be sure that this is what you want, before I spent an afternoon writing Stata code for you. Maarten -----Original Message----- From: [email protected] [mailto:[email protected]]On Behalf Of Reza C Daniels Sent: donderdag 29 september 2005 12:34 To: [email protected] Subject: Re: st: RE: Generating skewed distributions on closed intervals Hi Maarten, I tried this in the following way: set obs 100 -gen z1=invnorm(uniform())- where z>0 -gen z2=ln(z1)- for positively skewed -gen z3=exp(z1)- for negatively skewed As I'm sure you know, this gives me the correct shape of the distributions I'm looking for, but the incorrect range. So, I still can't solve it. Thanks anyway, Reza Maarten Buis wrote:`

`It reminds me of an ordered probit problem: you have one unobserved distribution, which is being carved up. Only now you also have information about where the cuts are made. This should be solvable. You might want to look at the log normal instead of the normal though, since no one can get, or has ever been, -2 (even with plastic surgery). -----Original Message----- From: [email protected] [mailto:[email protected]]On Behalf Of Nick Cox Sent: donderdag 29 september 2005 11:09 To: [email protected] Subject: RE: st: RE: Generating skewed distributions on closed intervals Well, I guess wildly the literature you are unaware of holds better solutions, but that's an empty comment as I don't know what it is. The idea that an age distribution is a bunch of little truncated Gaussians sitting next to each other on a line sounds at best strange to me, but as I said I don't understand what your problem is. Nick [email protected] Reza C Daniels`

There is a literature on this problem that I am aware of. I'm just having trouble with the code in Stata to generate my required results.Whatever your problem is, it is difficult to believe that there is not a literature on it, e.g. in demography, actuarial science, population ecology.* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**RE: st: RE: Generating skewed distributions on closed intervals***From:*"Maarten Buis" <[email protected]>

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