
KAPPENMAN RName:
The Kappenman's R statistic provides a test for distinguishing the lognormal model from the Weibull model. The test statistic is defined as
where
This test statistic is compared to the value 0.7477. If the test statistic is greater than this value, we choose the lognormal distribution. Otherwise we choose the Weibull distribution. The references listed below provide the justification for this statistic.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <a> is a parameter where the computed statistic is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <a> is a parameter where the computed statistic is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This command returns the cutoff value for Kappenman's statistic. Currently, this always returns 0.7477.
LET CV = KAPPENMAN R CUTOFF Y1
Kappenman's R is formulated as a selection problem with no preference for either the lognormal or the Weibull. On the other hand, the likelihood ratio test is formulated as a hypothesis test and tends to favor the distribution that is given as the null hypothesis. Neither test says anything about whether the lognormal or Weibull provides an adequate distributional model. They just answer the question about which of the two models is better. For that reason, whichever model is selected should still be examined for model adequacy (e.g., goodness of fit tests and probability plots).
McCool (2012), "Using the Weibull Distribution: Reliability, Modeling, and Inference," Wiley, pp. 207210. Dumonceaux and Antle (1973), "Discrimination Between the LogNormal and Weibull Distributions," Technometrics, Vol. 15, No. 4, pp. 923926.
. Step 1: Create the data for the example on page 925 of the . Dumonceaux and Antle Technometrics paper . serial read y 17.88 28.92 33.00 41.52 42.12 45.60 48.48 51.84 51.96 54.12 55.56 67.80 68.64 68.64 68.88 84.12 93.12 98.64 105.12 105.84 127.92 128.04 173.40 end of data . . Step 2: Perform Test . set write decimals 4 let r = kappenman r y let r = round(r,4) print "Kappenman R = ^r (cutoff = 0.7477)"The following output is generated Kappenman R = 0.7811 (cutoff = 0.7477)Program 2: . Step 1: Read data from p. 209 of McCool. . serial read y 1.4171126 2.8473605 3.1387760 3.6917256 3.9947116 4.5138741 2.4294320 2.8856396 3.1792441 3.7922064 4.2446643 4.615145 2.5617789 3.0469363 3.3558955 3.8552721 4.2881964 4.9614991 2.6524817 3.0654405 3.5946731 3.8881352 4.2953750 5.5373569 2.8297682 3.1045878 3.6295689 3.9605876 4.4814342 5.7385071 end of data . let y = exp(y) . let kappr = kappenman r y let kapcv = kappenman r cutoff y . let kappr = round(kappr,4) print "Kappenman R = ^r (cutoff = ^kapcv)"The following output is generated Kappenman R = 1.109 (cutoff = 0.7477)  
Privacy
Policy/Security Notice
NIST is an agency of the U.S. Commerce Department.
Date created: 01/31/2015 