PNRHAZ

PNRHAZ (LET)

Library Function

Compute the standard power-normal hazard function.

The standard power-normal distribution has the following hazard function:

where p is the power parameter, and and are the cumulative distribution function and the probability density function for the standard normal distribution respectively.

If p is 1, this distribution reduces to the normal distribution.

LET <y> = PNRHAZ(<x>,<p>)        <SUBSET/EXCEPT/FOR qualification>
where <x> is a number, parameter, or variable;
              <p> is a positive number, parameter, or variable that specifies the power parameter;
              <y> is a variable or a parameter (depending on what <x> is) where the computed power-normal hazard value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = PNRHAZ(3,2)
LET X2 = PNRHAZ(X1,POW)
LET X2 = PNRHAZ(X1,0.5)

The general form of the power-normal distribution is:

where and are the location and scale parameters, respectively.

None

None

PNRCDF	= Compute the power-normal cumulative distribution function.
PNRPDF	= Compute the power-normal probability density function.
PNRPPF	= Compute the power-normal percent point function.
PNRCHAZ	= Compute the power-normal cumulative hazard function.
PLNPDF	= Compute the power-lognormal probability density function.
LGNPDF	= Compute the lognormal probability density function.
NORPDF	= Compute the normal probability density function.

"A Computer Program POWNOR for Fitting the Power-Normal and -Lognormal Models to Life or Strength Data from Specimens of Various Sizes", Nelson and Doganaksoy, NIST-IR 4760, March 1992.

Reliability

1998/4

LABEL CASE ASIS
X1LABEL P
Y1LABEL Hazard
YLIMITS 0 1 
MAJOR YTIC MARK NUMBER 6 
TITLE CASE ASIS
TITLE Power Normal Hazard Plot CR() ...
 SD=1, P=10000, 3000, 1000, 300, 100, 50, 20, 5, 1, 0.5, 0.2 0.1 
. 
PLOT PNRHAZ(X,10000) FOR X = -5 .05 5 AND 
PLOT PNRHAZ(X,3000) FOR X = -5 .05 5 AND 
PLOT PNRHAZ(X,1000) FOR X = -5 .05 5 AND 
PLOT PNRHAZ(X,300) FOR X = -5 .05 5 AND 
PLOT PNRHAZ(X,100) FOR X = -5 .05 5 AND 
PLOT PNRHAZ(X,50) FOR X = -5 .05 5 AND 
PLOT PNRHAZ(X,20) FOR X = -5 .05 5 AND 
PLOT PNRHAZ(X,5) FOR X = -5 .05 5 AND 
PLOT PNRHAZ(X,1) FOR X = -5 .05 5 AND 
PLOT PNRHAZ(X,0.5) FOR X = -5 .05 5 AND 
PLOT PNRHAZ(X,0.2) FOR X = -5 .05 5 AND 
PLOT PNRHAZ(X,0.1) FOR X = -5 .05 5