 Dataplot Vol 2 Vol 1

# PARHAZ

Name:
PARHAZ (LET)
Type:
Library Function
Purpose:
Compute the Pareto hazard function with shape parameters and a.
Description:
The standard form of the Pareto hazard function is: with and a denoting the tail length shape parameter and the lower bound parameter, respectively.

Note that although the a parameter is typically called a location parameter (and it is in the sense that it defines the lower bound), it is not a location parameter in the technical sense that the following relation does not hold: with h denoting the hazard function.

For this reason, Dataplot treats a as a shape parameter. In Dataplot, the a shape parameter is optional with a default value of 1.

Syntax:
LET <y> = PARHAZ(<x>,<gamma>,<a>,<loc>,<scale>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a variable, a number, or a parameter;
<gamma> is a number or parameter that specifies the tail length shape parameter;
<a> is a number or parameter that specifies the optional lower bound shape parameter;
<loc> is a number or parameter that specifies the optional location parameter;
<scale> is a number or parameter that specifies the optional scale parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed Pareto hazard value is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The a, loc, and scale parameters are all optional.

Examples:
LET A = PARHAZ(3,1.5)
LET A = PARHAZ(3,1.5,2)
LET Y = PARHAZ,GAMMA,A,LOC,SCALE)
PLOT PARHAZ(X,GAMMA,A,LOC,SCALE) FOR X = XSTART 0.01 XSTOP
Note:
The Pareto hazard function can be extended with location and scale parameters by using the relationship Most applications of the Pareto distribution use the standard form (location = zero, scale = one).

Default:
None
Synonyms:
None
Related Commands:
 PARCDF = Compute the Pareto cumulative distribution function. PARCHAZ = Compute the Pareto cumulative hazard function. PARPDF = Compute the Pareto probability density function. PARPPF = Compute the Pareto percent point function. GEPPDF = Compute the generalized Pareto probability density function. EV1PDF = Compute the extreme value type I probability density function. WEIPDF = Compute the Weibull probability density function. EXPPDF = Compute the exponential probability density function.
Reference:
"Continuous Univariate Distributions: Volume 1", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 19.
Applications:
Distributional Modeling
Implementation Date:
1998/4
Program:
```
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
.
CASE ASIS
TITLE CASE ASIS
LABEL CASE ASIS
TITLE DISPLACEMENT 2
Y1LABEL DISPLACEMENT 15
X1LABEL DISPLACEMENT 12
Y1LABEL Hazard
X1LABEL X
.
TITLE Gamma = 1
PLOT PARHAZ(X,1) FOR X = 1 0.1 10
TITLE Gamma = 2
PLOT PARHAZ(X,2) FOR X = 1 0.1 10
TITLE Gamma = 5
PLOT PARHAZ(X,5) FOR X = 1 0.1 10
TITLE Gamma = 0.5
PLOT PARHAZ(X,0.5) FOR X = 1 0.1 10
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATION CENTER
TEXT Pareto Hazard Functions
``` Date created: 8/23/2006
Last updated: 8/23/2006