
DIWPDFName:
with q and denoting the shape parameters. This distribution has application in reliability when the response of interest is a discrete variable.
<SUBSET/EXCEPT/FOR qualification> where <x> is a positive integer variable, number, or parameter; <q> is a number, parameter, or variable in the range (0,1) that specifies the first shape parameter; <beta> is a number, parameter, or variable that specifies the second shape parameter; <y> is a variable or a parameter (depending on what <x> is) where the computed discrete Weibull pdf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y = DIWPDF(X,0.3,0.7) PLOT DIWPDF(X,0.6,0.4) FOR X = 1 1 20
LET Q = <value> LET BETA = <value> LET Y = DISCRETE WEIBULL ... RANDOM NUMBERS FOR I = 1 1 N
DISCRETE WEIBULL PROBABILITY PLOT Y
DISCRETE WEIBULL CHISQUARE ... You can generate estimates of q and based on the maximum ppcc value or the minimum chisquare goodness of fit with the commands
LET Q2 = <value> LET BETA1 = <value> LET BETA2 = <value> DISCRETE WEIBULL KS PLOT Y DISCRETE WEIBULL KS PLOT Y2 X2 DISCRETE WEIBULL KS PLOT Y3 XLOW XHIGH DISCRETE WEIBULL PPCC PLOT Y DISCRETE WEIBULL PPCC PLOT Y2 X2 DISCRETE WEIBULL PPCC PLOT Y3 XLOW XHIGH The default values of Q1 and Q2 are 0.05 and 0.95, respectively. The default values for beta1 and beta2 are 0.1 and 3, respectively. Due to the discrete nature of the percent point function for discrete distributions, the ppcc plot will not be smooth. For that reason, if there is sufficient sample size the KS PLOT (i.e., the minimum chisquare value) is typically preferred. However, it may sometimes be useful to perform one iteration of the PPCC PLOT to obtain a rough idea of an appropriate neighborhood for the shape parameters since the minimum chisquare statistic can generate extremely large values for nonoptimal values of the shape parameters. Also, since the data is integer values, one of the binned forms is preferred for these commands.
Nakagawa and Osaki (1975), "The Discrete Weibull Distribution", IEEE Transactions on Reliability, R24, pp. 300301.
title size 3 tic label size 3 label size 3 legend size 3 height 3 x1label displacement 12 y1label displacement 15 . multiplot corner coordinates 0 0 100 95 multiplot scale factor 2 label case asis title case asis case asis tic offset units screen tic offset 3 3 title displacement 2 y1label Probability Mass x1label X . ylimits 0 0.2 major ytic mark number 5 minor ytic mark number 4 xlimits 0 20 line blank spike on . multiplot 2 2 . title Q = 0.3, Beta = 0.3 plot diwpdf(x,0.3,0.3) for x = 1 1 20 . title Q = 0.5, Beta = 0.5 plot diwpdf(x,0.5,0.5) for x = 1 1 20 . title Q = 0.7, Beta = 0.7 plot diwpdf(x,0.7,0.7) for x = 1 1 20 . title Q = 0.9, Beta = 0.9 plot diwpdf(x,0.9,0.9) for x = 1 1 20 . end of multiplot . justification center move 50 97 text Probability Mass Functions for Discrete Weibull Program 2: let q = 0.4 let beta = 0.5 . let y = discrete weibull rand numbers for i = 1 1 500 . let xmax = maximum y let xmax2 = xmax + 0.5 let xmin = minimum y class lower 0.5 class upper xmax2 class width 1 . let y2 x2 = binned y let y3 xlow xhigh = combine frequency table y2 x2 . char blank line solid y1label Minimum ChiSquare x1label Beta (curves represent values of Q) discrete weibull ks plot y3 xlow xhigh justification center move 50 6 text Minimum ChiSquare = ^minks . let q = shape1 let beta = shape2 char x line blank y1label Data x1label Theoretical discrete weibull prob plot y2 x2 justification center move 50 6 text PPCC = ^ppcc . line solid characters blank relative hist y2 x2 limits freeze preerase off line color blue plot diwpdf(x,q,beta) for x = 0 1 xmax preerase on limits . discrete weibull chisquare goodness of fit y3 xlow xhighThe following graphs and output are generated. CHISQUARED GOODNESSOFFIT TEST NULL HYPOTHESIS H0: DISTRIBUTION FITS THE DATA ALTERNATE HYPOTHESIS HA: DISTRIBUTION DOES NOT FIT THE DATA DISTRIBUTION: DISCRETE WEIBULL SAMPLE: NUMBER OF OBSERVATIONS = 500 NUMBER OF NONEMPTY CELLS = 13 NUMBER OF PARAMETERS USED = 2 TEST: CHISQUARED TEST STATISTIC = 7.480574 DEGREES OF FREEDOM = 10 CHISQUARED CDF VALUE = 0.320571 ALPHA LEVEL CUTOFF CONCLUSION 10% 15.98718 ACCEPT H0 5% 18.30704 ACCEPT H0 1% 23.20925 ACCEPT H0
Date created: 11/16/2006 