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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

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

Subject |
RE: st: evaluating probabilities using kdensity |

Date |
Mon, 3 Mar 2008 14:55:42 -0000 |

In addition, and to pick up comments Maarten made when this was first asked, I don't see that you are obliged to work via the density function at all when the overall aim is to get an integral like this. A (possibly smoothed) quantile function and a distribution function are just inverses of each other. Nick n.j.cox@durham.ac.uk Maarten buis *---------- begin example ------------- sysuse auto, clear kdensity mpg, gen(x d) n(100) integ d x if x < 20 *------------- end example ------------ (For more on how to use examples I sent to the Statalist, see http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html ) Conner Mullally <mullally@primal.ucdavis.edu> wrote: > Thanks for the help. I think I could have been more specific > about exactly what I am trying to do. > I have 20 years of time series, which I have detrended. > What I want to do is to: > a) Take the detrended time series and estimate a kernel > density > b) Use the estimated kernel density to estimate the expected > value of shortfalls from the mean of the distribution. That > is, I want to calculate the integral of: > (Mu-Yt)dF(Yt)dYt, for all Yt<Mu > Where Mu is the mean, Yt is the random variable, and F(Yt) > is the cumulative density function of Yt. > The command kdensity returns the estimated density at > whatever points were used to estimate the density, and I can > add more points using the at() option. But these will leave > gaps at the omitted points in the support of the estimated > distribution when I sum up the densities. What I'm > wondering is if there is a way to integrate under the curve > of the estimated kernel density. Perhaps some stata > programming is in my future, but if there is way to do this > while using kdensity or something similar, I would love to > know. * * 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: evaluating probabilities using kdensity***From:*"Conner Mullally" <mullally@primal.ucdavis.edu>

**Re: st: evaluating probabilities using kdensity***From:*Maarten buis <maartenbuis@yahoo.co.uk>

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