LEXPPF

LEXPPF (LET)

Library Function

Compute the logistic-exponential percent point function with shape parameter .

The standard logistic-exponential distribution has the following percent point function:

with denoting the shape parameter. Note that if < 1, then 0 < p < 1.

This distribution can be generalized with location and scale parameters in the usual way using the relation

with and denoting the location and scale parameters, respectively.

LET <y> = LEXPPF(<p>,<beta>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <p> is a number, parameter, or variable in the interal (0,1];
            <y> is a variable or a parameter (depending on what <p> is) where the computed logistic-exponential ppf value is stored;
            <beta> is a number, parameter, or variable that specifies the shape parameter;
            <loc> is a number, parameter, or variable that specifies the location parameter;
            <scale> is a positive number, parameter, or variable that specifies the scale parameter;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

If <loc> and <scale> are omitted, they default to 0 and 1, respectively.

LET A = LEXPPF(0.95,0.2)
LET Y = LEXPPF(P,0.5,0,5)
PLOT LEXPPF(P,2.7,0,3) FOR P = 0 0.01 0.99

None

None

LEXCDF	= Compute the logistic-exponential cumulative distribution function.
LEXCHAZ	= Compute the logistic-exponential cumulative hazard function.
LEXHAZ	= Compute the logistic-exponential hazard function.
LEXPDF	= Compute the logistic-exponential probability density function.
RAYPDF	= Compute the Rayleigh probability density function.
WEIPDF	= Compute the Weibull probability density function.
LGNPDF	Compute the lognormal probability density function.
EXPPDF	= Compute the exponential probability density function.
LOGPDF	= Compute the logistic probability density function.
GAMPDF	= Compute the gamma probability density function.
EWEPDF	= Compute the exponentiated Weibull probability density function.
B10PDF	= Compute the Burr type 10 probability density function.

Leemis and McQuestion (2008), "Univariate Distribution Relationships", The American Statistician, Vol. 62, No. 1, pp. 45-53.

Lan and Leemis (2008), "The Logistic-Exponential Survival Distribution", Naval Research Logistics, to appear.

Distributional Modeling

2008/2

 
LABEL CASE ASIS
TITLE CASE ASIS
TITLE OFFSET 2
.
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
.
LET BETA  = 0.5
TITLE BETA = ^BETA
PLOT LEXPPF(P,BETA) FOR P = 0.01  0.01  0.99
.
LET BETA  = 1
TITLE BETA = ^BETA
PLOT LEXPPF(P,BETA) FOR P = 0.01  0.01  0.99
.
LET BETA  = 2
TITLE BETA = ^BETA
PLOT LEXPPF(P,BETA) FOR P = 0.01  0.01  0.99
.
LET BETA  = 5
TITLE BETA = ^BETA
PLOT LEXPPF(P,BETA) FOR P = 0.01  0.01  0.99
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Logistic-Exponential Percent Point Functions