
COMMON WEIBULL SHAPE PARAMETERName:
Before applying the test described here, each of the samples should be tested to ensure that they can in fact be adequately modeled with a 2parameter Weibull distribution. If not, then applying this test is not meaningful. Given k samples, the test procedure is as follows.
<SUBSET/EXCEPT/FOR qualification> where <y> is a response variable; <tag> is a groupid variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The response variable and the groupid variables should have the same number of observations.
<SUBSET/EXCEPT/FOR qualification> where <y1> ... <yk> is a list of 2 to 30 response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The response variables do not need to have equal sample sizes.
<SUBSET/EXCEPT/FOR qualification> where <y> is a response variable; <x1> ... <xk> is a list of 1 to 6 groupid variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. All variables should have the same number of observations.
REPLICATED COMMON WEIBULL SHAPE PARAMETER Y X1 X2 MULTIPLE COMMON WEIBULL SHAPE PARAMETER Y1 TO Y5 COMMON WEIBULL SHAPE PARAMETER Y X SUBSET X > 1
LET A = COMMON WEIBULL SHAPE TEST CDF Y X LET A = COMMON WEIBULL SHAPE TEST PVALUE Y X LET A = COMMON WEIBULL SHAPE TEST CV90 Y X LET A = COMMON WEIBULL SHAPE TEST CV95 Y X LET A = COMMON WEIBULL SHAPE TEST CV99 Y X Dataplot statistics can be used in a number of commands. For details, enter
where <value> is 0.90, 0.95, or 0.99. If this command is not given, the default value for alpha will be 0.95. The equation used to estimate the common shape parameter is given on page 238 of McCool. If a common shape parameter is estimated, then the corresponding scale parameters for each of the groups based on this common shape parameter are written to the file "dpst1f.dat".
Dataplot currently only supports the uncensored data case. Dataplot performs the simulations for the critical values dynamically, so it does not require equal sample sizes for the groups.
. Step 1: Read the data . skip 25 read mccool82.dat y1 y2 y3 y4 y5 let y x = stack y1 y2 y3 y4 y5 set write decimals 5 set minmax 1 . . Step 2: Perform the command . common weibull shape test y xThe following output is generated. Test for Common Weibull Shape Parameter (For the 2Parameter Weibull Distribution) Response Variable: Y GroupID Variable: X H0: Homogeneous Shape Parameters Ha: Shape Parameters Are Not Homogeneous Summary Statistics: Total Number of Observations: 50 Number of Groups: 5 Number of Groups Used in Test: 5 Minimum Value of Shape Parameter: 1.93917 Maximum Value of Shape Parameter: 3.65176 Test Statistic Value: 1.88316 CDF of Test Statistic: 0.53140 PValue: 0.46860 Estimate of Common Shape Parameter: 2.48034 Percent Points of the Reference Distribution  Percent Point Value  0.0 = 0.000 50.0 = 1.845 75.0 = 2.200 90.0 = 2.640 95.0 = 2.986 97.5 = 3.265 99.0 = 3.726 99.9 = 5.094 Conclusions (Upper 1Tailed Test)  Alpha CDF Critical Value Conclusion  10% 90% 2.640 Accept H0 5% 95% 2.986 Accept H0 2.5% 97.5% 3.265 Accept H0 1% 99% 3.726 Accept H0 Confidence Interval for Common Shape Parameter  Confidence Lower Upper Coefficient Limit Limit  50.00 2.12965 2.49122 80.00 1.97370 2.67145 90.00 1.88467 2.77648 95.00 1.80180 2.88262 99.00 1.65531 3.09005 99.90 1.50608 3.32405  . . Step 3: Compute the test statistic . let statval = common weibull shape test y x let statcdf = common weibull shape test cdf y x let pval = common weibull shape test pvalue y x let cv90 = common weibull shape test cv90 y x . print statval statcdf pval cv90The following output is generated. PARAMETERS AND CONSTANTS STATVAL  1.88316 STATCDF  0.53120 PVAL  0.46260 CV90  2.63340  
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Date created: 09/11/2014 