Dataplot Vol 2 Vol 1

# QBIPPF

Name:
QBIPPF (LET)
Type:
Library Function
Purpose:
Compute the quasi-binomial type I percent point function.
Description:
The quasi-binomial type I distribution has the following probability mass function:

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:

The percent point function is computed by summing the cumulative distribution function until the appropriate probability is obtained.

Syntax:
LET <y> = QBIPPF(<x>,<p>,<theta>,<beta>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a variable, number, or parameter in the interval (0,1);
<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 ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = QBIPPF(0.95,0.5,0.005,20)
LET Y = QBIPPF(P,0.7,0.01,20)
PLOT QBIPPF(P,0.3,0.005,20) FOR P = 0 0.01 1
Default:
None
Synonyms:
None
Related Commands:
 QBICDF = Compute the quasi-binomial type I cumulative distribution function. QBIPDF = Compute the quasi-binomial type I probability mass function. BINPDF = Compute the binomial probability mass function. BBNPDF = Compute the beta-binomial probability mass function. NBPDF = Compute the negative binomial probability mass function.
Reference:
Consul and Famoye (2006), "Lagrangian Probability Distribution", Birkhauser, pp. 70-80.
Applications:
Distributional Modeling
Implementation Date:
2006/8
Program:
```
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
x1label Probability
y1label X
.
xlimits 0 1
major xtic mark number 6
minor xtic mark number 3
.
multiplot 2 2
.
title P = 0.3, Phi = 0.01, M = 20
plot qbicdf(x,0.3,0.01,20) for x = 0  0.01  1
.
title P = 0.3, Phi = -0.01, M = 20
let phi = -0.01
plot qbicdf(x,0.3,phi,20) for x = 0  0.01  1
.
title P = 0.7, Phi = 0.01, M = 20
plot qbicdf(x,0.7,0.01,20) for x = 0  0.01  1
.
title P = 0.7, Phi = -0.01, M = 20
let phi = -0.01
plot qbicdf(x,0.7,phi,20) for x = 0  0.01  1
.
end of multiplot
.
justification center
move 50 97
text Percent Point Functions for Quasi Binomial Type I
```

Date created: 8/23/2006
Last updated: 8/23/2006