PNRPDF

PNRPDF (LET)

Library Function

Compute the standard power-normal probability density function.

The standard power-normal distribution has the following probability density 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 <y2> = PNRPDF(<y1>,<p>)        <SUBSET/EXCEPT/FOR qualification>
where <y1> is a number, parameter, or variable;
              <p> is a positive number, parameter, or variable that specifies the power parameter;
              <y2> is a variable or a parameter (depending on what <y1> is) where the computed power-normal pdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

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

The general power-normal distribution has the following probability density function:

where and are the location and scale parameters, respectively.

None

None

PNRCDF	= Compute the power-normal cumulative distribution function.
PNRPPF	= Compute the power-normal percent point function.
PNRHAZ	= Compute the power-normal hazard function.
PNRCHAZ	= Compute the power-normal cumulative hazard function.
PLNCDF	= Compute the power-lognormal cumulative distribution function.
PLNPDF	= Compute the power-lognormal probability density function.
PLNPPF	= Compute the power-lognormal percent point function.
LGNCDF	= Compute the lognormal cumulative distribution function.
LGNPDF	= Compute the lognormal probability density function.
LGNPPF	= Compute the lognormal percent point function.
NORCDF	= Compute the normal cumulative distribution function.
NORPDF	= Compute the normal probability density function.
NORPPF	= Compute the normal percent point 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

1995/5

LABEL CASE ASIS
X1LABEL X
YLIMITS 0 1.5
Y1LABEL Probability
MAJOR YTIC MARK NUMBER 6 
TITLE CASE ASIS
TITLE Power Normal PDF Plot CR() ...
 SD=1, P=10000, 3000, 1000, 300, 100, 50, 20, 5, 1, 0.5, 0.2 0.1 
. 
PLOT PNRPDF(X,10000) FOR X = -5 .05 5 AND 
PLOT PNRPDF(X,3000) FOR X = -5 .05 5 AND 
PLOT PNRPDF(X,1000) FOR X = -5 .05 5 AND 
PLOT PNRPDF(X,300) FOR X = -5 .05 5 AND 
PLOT PNRPDF(X,100) FOR X = -5 .05 5 AND 
PLOT PNRPDF(X,50) FOR X = -5 .05 5 AND 
PLOT PNRPDF(X,20) FOR X = -5 .05 5 AND 
PLOT PNRPDF(X,5) FOR X = -5 .05 5 AND 
PLOT PNRPDF(X,1) FOR X = -5 .05 5 AND 
PLOT PNRPDF(X,0.5) FOR X = -5 .05 5 AND 
PLOT PNRPDF(X,0.2) FOR X = -5 .05 5 AND 
PLOT PNRPDF(X,0.1) FOR X = -5 .05 5