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From |
Steve Samuels <sjsamuels@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: RE: How to test whether data follows Exp distribution? |

Date |
Wed, 7 Jul 2010 10:25:42 -0400 |

"3. You can -stset- your variable as if it were a survival time and follow with -streg, d(e)- specifying just the response, and no predictors." -streg, d(e)- will return I think this is what Nick had in mind:'' ************************* set more off webuse kva, clear streg, d(e) //exponential, no parameters streg, d(e) nohr // exponential log hazard streg, d(w) nohr //weibull streg, d(w) nohr vce(robust) // weibull ************************* The test that ln_p = 0 from the last 2 commands is a test of the weibull versus the exponential. For a test against parametric alternatives, There are other one-parameter generalizations of the exponential distribution, including gamma (in -streg-), Pareto, Rayleigh. I would also guess that Lambert and Royston's flexible spline models (-stpm- -stpm2- from SSC) can provide a test of a constant hazard function. Steve -- Steven Samuels sjsamuels@gmail.com 18 Cantine's Island Saugerties NY 12477 USA Voice: 845-246-0774 Fax: 206-202-4783 On Wed, Jul 7, 2010 at 6:33 AM, Nick Cox <n.j.cox@durham.ac.uk> wrote: > You're meant to knit your own alternative cumulative for the right-hand > side. The > equivalent would be > > ksmirnov x = 1 - exp(-x/r(mean)) > > These tests loom large in mathematical statistics texts. (The prestige > of Kolmogorov as one of the giants of probability theory and the > generality and elegance of the underlying idea have, I guess, not > hindered their survival from text to text.) But in my view they are not > much use in practical data analysis: > > 1. Using parameters estimated from the data, as is typical, has worried > some statisticians in the past. The orthodox calculation presumes that > parameter values are somehow known. The manual entry makes light of > this, but it should be mentioned. > > 2. More importantly, and as the manual entry does make clear, these > tests are not much use for picking up deviations in the tails. (Observed > and expected cumulatives necessarily both converge to 0 and 1 in the two > tails.) For work with distributions like the exponential, what is going > on in the far tail is very likely to be of great concern both > scientifically and statistically. > > 3. A test result does not indicate exactly what is going on. Knowing the > reason for rejection -- or of failure to reject -- will be of more > guidance to your data analysis than getting a P-value. Graphs are > critical here, as Maarten flags. > > There are plenty of alternatives, however. In addition to Maarten's > -hangroot-, > > 1. -qexp- and -pexp- from SSC offer canned Q-Q and P-P plots for the > exponential. Note that > > SJ-7-2 gr0027 . . Stata tip 47: Quantile-quantile plots without > programming > . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. > J. Cox > Q2/07 SJ 7(2):275--279 (no > commands) > tip on producing various quantile-quantile (Q-Q) plots > > is now available to all, regardless of whether you subscribe to the SJ, > given the SJ's 3-year moving window. This short paper explains the logic > of Q-Q plots, gives references and includes the exponential as one of > its examples. > > To help assess the lack of fit, you can easily produce a portfolio of > plots for random samples of the same size from an exponential: > > sysuse auto, clear > > qexp price, saving(price) > > forval i = 1/24 { > gen exp`i' = -ln(runiform()) > qexp exp`i', saving(g`i') > local names `names' "g`i'" > } > > graph combine "price" `names' > > 2. -dpplot- (SJ) is another graphical approach. > > 3. You can -stset- your variable as if it were a survival time and > follow with -streg, d(e)- specifying just the response, and no > predictors. The information given bears indirectly on the question, but > this is a formal test of exponentiality, as I understand it. Survival > experts will be able to expand (or to rebut). > > Nick > n.j.cox@durham.ac.uk > > Maarten L. Buis > > You can use -hangroot- to check an empirical distribution against, among > others, an exponential distribution. To install it type in Stata -ssc > install hangroot-. > > Jabr, Wael M > > I am trying to find if the variable I have follows an exponential > distribution. Tried to locate some goodness of fit tests but wasn't > successful. > After some long search I found the command ksmirnov. However, the help > doesn't offer much on how to use it. They have an illustration for > testing if a variable x follows normal distribution. > > ksmirnov x = normal((x-r(mean))/r(sd)) > > > * > * 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: How to test whether data follows Exp distribution?***From:*"Jabr, Wael M" <wael.jabr@student.utdallas.edu>

**st: RE: How to test whether data follows Exp distribution?***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

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