PEXCHAZ

PEXCHAZ (LET)

Library Function

Compute the exponential power cumulative hazard function with shape parameter .

The exponential power distribution has the following cumulative hazard function:

with denoting the shape parameter.

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

This distribution was proposed by Dhillon as useful distribution for reliability applications since it can have increasing, decreasing, or bathtub shaped hazard functions.

LET <y> = PEXCHAZ(<x>,<beta>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <x> is a number, parameter, or variable containing positive values;
            <y> is a variable or a parameter (depending on what <x> is) where the computed exponential power cumulative hazard value is stored;
            <beta> is a positive 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 = PEXCHAZ(0.3,2.5)
LET A = PEXCHAZ(X1,2.5,0,10)
PLOT PEXCHAZ(X,2.5,0,3) FOR X = 0.1 0.1 10

The 11/2007 version changed the syntax for this function from
LET A = PEXCHAZ(X,ALPHA,BETA,LOC,SCALE)

to

LET A = PEXCHAZ(X,BETA,LOC,SCALE)

This was done since ALPHA is in fact a scale parameter (in the articles listed in the References section, ALPHA is actually the reciprocal of the scale parameter).

None

None

PEXPDF	= Compute the exponential power probability density function.
PEXCDF	= Compute the exponential power cumulative distribution function.
PEXPPF	= Compute the exponential power percent point function.
PEXHAZ	= Compute the exponential power hazard function.
ALPPDF	= Compute the alpha probability density function.
WEIPDF	= Compute the Weibull probability density function.
LGNPDF	= Compute the log-normal probability density function.
NORPDF	= Compute the normal probability density function.

Johnson, Kotz, and Balakrishnan (1994), "Continuous Univariate Distributions--Volume 2", Second Edition, John Wiley and Sons, pp. 643-644.

Dhillon (1981), "Life Distributions", IEEE Transactions on Reliability, Vol. R-30, No. 5, pp. 457-459.

Reliability, accelerated life testing

1998/4
2007/11: Corrected the second shape parameter to be the scale parameter

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 PEXCHAZ(X,BETA) FOR X = 0.01  0.01  2
.
LET BETA  = 1
TITLE BETA = ^beta
PLOT PEXCHAZ(X,BETA) FOR X = 0.01  0.01  2
.
LET BETA  = 2
TITLE BETA = ^beta
PLOT PEXCHAZ(X,BETA) FOR X = 0.01  0.01  2
.
LET BETA  = 5
TITLE BETA = ^beta
PLOT PEXCHAZ(X,BETA) FOR X = 0.01  0.01  2
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Exponential Power Cumulative Hazard Functions