with p, , and m denoting the shape parameters.
The quasi-binomial type I distribution is used to model Bernoulli trials. The parameter p denotes the initial probability of success, m denotes the number of Bernoulli trials, and denotes how the probability of success increases or decreases with the number of successes. Specificially, when = 0, the quasi-binomial type I distribution reduces to the binomial distribution. When ≠ 0, the probability of success in the xth trial becomes
The cumulative distribution function is computed using the following recurrence relation given by Consul and Famoye:
where <x> is a positive integer variable, number, or parameter;
<p> is a number, parameter, or variable in the range (0,1) that specifies the first shape parameter;
<phi> is a number, parameter, or variable that specifies the second shape parameter;
<m> is a number, parameter, or variable that specifies the third shape parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed quasi binomial type I cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y = QBICDF(X,0.7,0.01,20)
PLOT QBICDF(X,0.3,0.005,20) FOR X = 0 1 20
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 x1label X . ylimits 0 1 major ytic mark number 6 minor ytic mark number 3 xlimits 0 20 line blank spike on . multiplot 2 2 . title P = 0.3, Phi = 0.01, M = 20 plot qbicdf(x,0.3,0.01,20) for x = 1 1 20 . title P = 0.3, Phi = -0.01, M = 20 let phi = -0.01 plot qbicdf(x,0.3,phi,20) for x = 1 1 20 . title P = 0.7, Phi = 0.01, M = 20 plot qbicdf(x,0.7,0.01,20) for x = 1 1 20 . title P = 0.7, Phi = -0.01, M = 20 let phi = -0.01 plot qbicdf(x,0.7,phi,20) for x = 1 1 20 . end of multiplot . justification center move 50 97 text Cumulative Distribution Functions for Quasi Binomial Type I
Date created: 8/23/2006