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

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

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

Date |
Wed, 7 Jul 2010 11:33:18 +0100 |

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/

**Follow-Ups**:**Re: st: RE: How to test whether data follows Exp distribution?***From:*Steve Samuels <sjsamuels@gmail.com>

**References**:**st: How to test whether data follows Exp distribution?***From:*"Jabr, Wael M" <wael.jabr@student.utdallas.edu>

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