LEXCHAZ

LEXCHAZ (LET)

Library Function

Compute the logistic-exponential cumulative hazard function with shape parameter .

The standard logistic-exponential distribution has the following cumulative hazard function:

with denoting the shape parameter.

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> = LEXCHAZ(<x>,<beta>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <x> is a number, parameter, or variable;
            <y> is a variable or a parameter (depending on what <x> is) where the computed logistic-exponential cumulative hazard 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 = LEXCHAZ(0.3,0.2)
LET Y = LEXCHAZ(X,0.5,0,5)
PLOT LEXCHAZ(X,0.7,0,3) FOR X = 0 0.01 5

None

None

LEXCDF	= Compute the logistic-exponential cumulative distribution function.
LEXHAZ	= Compute the logistic-exponential hazard function.
LEXPDF	= Compute the logistic-exponential probability density function.
LEXPPF	= Compute the logistic-exponential percent point 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 LEXCHAZ(X,BETA) FOR X = 0.01  0.01  5
.
LET BETA  = 1
TITLE BETA = ^BETA
PLOT LEXCHAZ(X,BETA) FOR X = 0.01  0.01  5
.
LET BETA  = 2
TITLE BETA = ^BETA
PLOT LEXCHAZ(X,BETA) FOR X = 0.01  0.01  5
.
LET BETA  = 5
TITLE BETA = ^BETA
PLOT LEXCHAZ(X,BETA) FOR X = 0.01  0.01  5
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Logistic-Exponential Cumulative Hazard Functions