Dataplot Vol 2 Vol 1

# LOSCDF

Name:
LOSCDF (LET)
Type:
Library Function
Purpose:
Compute the lost games cumulative distribution function.
Description:
The formula for the lost games probability mass function is

with p and r denoting the shape parameters. The r parameter is restricted to non-negative integers.

The cumulative distribution function is computed by summing the probability mass function.

Syntax:
LET <y> = LOSCDF(<x>,<p>,<r>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a positive integer variable, number, or parameter;
<p> is a number or parameter in the range (0.5,1) that specifies the first shape parameter;
<r> is a number or parameter denoting a positive integer that specifies the second shape parameter;
<y> is a variable or a parameter where the computed lost games cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = LOSCDF(3,0.7,3)
LET Y = LOSCDF(X1,0.7,2)
PLOT LOSCDF(X,0.6,5) FOR X = 5 1 50
Default:
None
Synonyms:
None
Related Commands:
 LOSPDF = Compute the lost games probability mass function. LOSPPF = Compute the lost games percent point function. BTAPDF = Compute the Borel-Tanner probability mass function. POIPDF = Compute the Poisson probability mass function. HERPDF = Compute the Hermite probability mass function. BINPDF = Compute the binomial probability mass function. NBPDF = Compute the negative binomial probability mass function. GEOPDF = Compute the geometric probability mass function.
Reference:
Luc Devroye (1986), "Non-Uniform Random Variate Generation", Springer-Verlang, pp. 758-759.

Kemp and Kemp (1968), "On a Distribution Associated with Certain Stochastic Processes", Journal of the Royal Statistical Society, Series B, 30, pp. 401-410.

Haight (1961), "A Distribution Analogous to the Borel-Tanner Distribution", Biometrika, 48, pp. 167-173.

Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 445-447.

Applications:
Distributional Modeling
Implementation Date:
2006/6
Program:
```
title size 3
tic label size 3
label size 3
legend size 3
height 3
multiplot scale factor 1.5
x1label displacement 12
y1label displacement 17
.
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 = 0.6, R = 3
plot loscdf(x,0.6,3) for x = 1 1 20
.
title P = 0.7, R = 3
plot loscdf(x,0.7,3) for x = 1 1 20
.
title P = 0.8, R = 3
plot loscdf(x,0.8,3) for x = 1 1 20
.
title P = 0.9, R = 3
plot loscdf(x,0.9,3) for x = 1 1 20
.
end of multiplot
.
justification center
move 50 97
text Cumulative Distribution for Lost Games
```

Date created: 6/20/2006
Last updated: 6/20/2006