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From |
Maarten Buis <maartenlbuis@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: distribution test |

Date |
Tue, 30 Aug 2011 16:45:50 +0200 |

On Tue, Aug 30, 2011 at 11:13 AM, Nick Cox wrote: > In addition to Maarten's good advice, and setting aside the question > of covariates, not mentioned in the original, at least as quoted here: > > There is a direct method to check for fit to an exponential > distribution: a quantile-quantile plot. Another alternative is the probability-probability plot. The QQ-plot is good at detecting deviations in the tails of the distribution, while the PP-plot is good at detecting deviations at the center of the distribution. Just like the QQ-plot, I like to add a number of simulations assuming the model is correct to help assess how much deviation from the 45 degree line is to be expected. Below is an example how I would create such a graph in Stata: *------------------------- begin example ---------------------- // create some expnential data local lambda = 2 drop _all set obs 500 gen y = -1/`lambda'*ln(1-runiform()) label var y "observed" // estimate parameter sum y, meanonly local lambdahat = 1/r(mean) di as txt "ML estimate of lambda is: " /// as result `lambdahat' // create variables for pp-plot gen byte touse = !missing(y) sort y gen F = 1-exp(-`lambdahat'*y) label var F "observed" gen Psubi = sum(touse) replace Psubi = cond(F>=.,.,Psubi/(Psubi[_N]+1)) // create 20 random variables assuming the model is correct forvalues i = 1/20 { gen y`i' = -1/`lambdahat'*ln(1-runiform()) if touse gen F`i' = 1-exp(-`lambdahat'*y`i') sort y`i' drop y`i' gen Psubi`i' = sum(touse) replace Psubi`i' = cond(F>=.,.,Psubi`i'/(Psubi`i'[_N]+1)) #delim ; local gr `"`gr' || line F`i' Psubi`i', sort lstyle(solid) lcolor(gs12)"' ; #delim cr } // create the graph twoway `gr' || /// scatter F Psubi, /// aspect(1) msymbol(oh) || /// function reference = x, /// lstyle(solid) /// legend(order( 1 "simulations" 21 22 )) /// xtitle("Empirical Pr(Y {&le} y) = i/(N+1)") /// ytitle("theoretical Pr(Y {&le} y)") *-------------------------- end example ----------------------- (For more on examples I sent to the Statalist see: http://www.maartenbuis.nl/example_faq ) Hope this helps, Maarten -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * 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: distribution test***From:*Nick Cox <njcoxstata@gmail.com>

**References**:**st: distribution test***From:*Maarten Buis <maartenlbuis@gmail.com>

**Re: st: distribution test***From:*Nick Cox <njcoxstata@gmail.com>

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