POWHAZ

POWHAZ (LET)

Library Function

Compute the power function hazard function with shape parameter c.

The standard form of the hazard function is:

with c denoting the shape parameter.

This distribution can be extended with lower and upper bound parameters. If a and b denote the lower and upper bounds, respectively, then the location and scale parameters are:

location = a
scale = b - a


The general form of the distribution can then be found by using the relation

If X has a Pareto distribution, then 1/X has a power distribution. The power distribution is also a special case of the beta distribution where the second shape parameter is equal to 1 (the reflected power distribution is the special case of the beta distribution where the first shape parameter = 1).

LET <y> = POWHAZ(<x>,<c>,<a>,<b>)
                        <SUBSET/EXCEPT/FOR qualification>
where <x> is a number, parameter, or variable containing values in the interval (a,b);
            <y> is a variable or a parameter (depending on what <x> is) where the computed power hazard value is stored;
            <c> is a positive number, parameter, or variable that specifies the shape parameter;
            <a> is a number, parameter, or variable that specifies the lower limit;
            <b> is a number, parameter, or variable that specifies the upper limit;
            and where the <SUBSET/EXCEPT/FOR qualification> is optional.

If <a> and <b> are omitted, they default to 0 and 1, respectively.

LET A = POWHAZ(3,1.5)
LET X2 = POWHAZ(X1,C)

None

None

POWPDF	= Compute the power probability density function.
POWCDF	= Compute the power cumulative distribution function.
POWPPF	= Compute the power percent point function.
POWCHAZ	= Compute the power cumulative hazard function.
RPOPDF	= Compute the reflected power probability density function.
BETPDF	= Compute the beta probability density function.
TOPPDF	= Compute the Topp and Leone probability density function.
RGTPDF	= Compute the generalized reflected Topp and Leone probability density function.
GTLPDF	= Compute the generalized Topp and Leone probability density function.
TSPPDF	= Compute the two-sided power probability density function.
TRIPDF	= Compute the triangular probability density function.
TRAPDF	= Compute the trapezoid probability density function.
UNIPDF	= Compute the uniform probability density function.
JSBPDF	= Compute the Johnson SB probability density function.

Johnson, Kotz, and Balakrishnan (1994), "Continuous Univariate Distributions--Volume 1", Second Edition, John Wiley and Sons, p. 607.

Evans, Hastings, and Peacock (2000), "Statistical Distributions", Third Edition, John Wiley & Sons, chapter 33.

Distributional Modeling

2007/12

 
TITLE POWER FUNCTION HAZARD FUNCTIONS (0.1,  0.5, 1, 3, 10)
PLOT POWHAZ(X,0.1) FOR X = 0.01 0.01 1 AND
PLOT POWHAZ(X,0.5) FOR X = 0.01 0.01 1 AND
PLOT POWHAZ(X,1) FOR X = 0.01 0.01 1 AND
PLOT POWHAZ(X,3) FOR X = 0.01 0.01 1 AND
PLOT POWHAZ(X,10) FOR X = 0.01 0.01 1