st: Re: Features for Stata 14

["Liu,Zhong" <zhong1969@hotmail.com>]

Dear Maarten:

Thanks for your reply. But I do mean -normal(x)- rather than -normalden(x)-. 
The issue involved is that I want to employ Equation (5.7) at p.126 of a 
paper authored by Kenneth A. Small and Harvey S. Rosen (1981) in 
Econometrica, Vol. 49, No. 1 (Jan., 1981), pp. 105-130. The paper is titled 
"Applied Welfare Economics with Discrete Choice Models", which you can find 
it by following the weblike below:

http://www.jstor.org/discover/10.2307/1911129?uid=3737800&uid=2129&uid=2&uid=70&uid=4&sid=21102620779363

And I also think that it is better for STATA to have an observation-level 
numerical integration since many simulation-based estimates need the 
functionality of the kind.

Best,
Zhong

-----原始邮件----- 
From: Maarten Buis
Sent: Thursday, September 05, 2013 3:48 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Re: Features for Stata 14

On Thu, Sep 5, 2013 at 8:40 AM, Liu,Zhong  wrote:
> A dataset has two variables, say ‘v1’ and ‘v2’. Either of them has ‘N’ 
>
> number of observations. I want to generate a third variable, say ‘v3’. 
> The
> 1st element of ‘v3’ is the numerical integration with the 1st element of
> ‘v1’ as the lower limit to the integral and the 1st element of ‘v2’ as 
> the
> upper limit to the integral. Similarly, the 2nd element of ‘v3’ is the
> numerical integration with the 2nd element of ‘v1’ as the lower limit to 
> the
> integral and the 2nd element of ‘v2’ as the upper limit. And so on. The
> function integrand is known STATA function such as 'normal(x)' or defined 
> by
> a program written by users.

For many distributions there is no need to do this numerically. In
your example, I suppose you mean -normalden(x)- for the function that
is to be integrated instead of -normal(x)-. -normalden()- gives you
the PDF of the normal distribution (the well known bell shaped curve),
while -normal()- gives you the CDF (an S-shaped curve). In that case
the solution is straightforward, as you can see in the example below.
In -help density_functions- you can find a list of distributions for
which this solution has been implemented.

*------------------ begin example ------------------
// create some example data
clear
input v1 v2
-2 2
-1 1
end

// compute your integrals
gen v3 = normal(v2) - normal(v1)

// admire the result
list
*------------------- end example -------------------
* (For more on examples I sent to the Statalist see:
* http://www.maartenbuis.nl/example_faq )

Hope this helps,
Maarten

Ps. As you can read in the Statalist FAQ
(http://www.stata.com/support/faqs/resources/statalist-faq/#spell) it
is Stata not STATA.

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------

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