PNRCDF
Name:
Type:
Purpose:
Compute the standard powernormal cumulative distribution
function.
Description:
The standard powernormal distribution has the following
cumulative distribution function:
where p is the shape (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.
Syntax:
LET <y2> = PNRCDF(<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 powernormal cdf
value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = PNRCDF(3,2)
LET X2 = PNRCDF(X1,POW)
LET X2 = PNRCDF(X1,0.5)
Note:
The general powernormal distribution has the following
cumulative distribution function:
where and
are the
location and scale parameters, respectively.
Default:
Synonyms:
Related Commands:
PNRPDF

= Compute the powernormal probability density function.

PNRPPF

= Compute the powernormal percent point function.

PNRHAZ

= Compute the powernormal hazard function.

PNRCHAZ

= Compute the powernormal cumulative hazard function.

PLNCDF

= Compute the powerlognormal cumulative distribution
function.

PLNPDF

= Compute the powerlognormal probability density
function.

PLNPPF

= Compute the powerlognormal 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.

Reference:
"A Computer Program POWNOR for Fitting the PowerNormal and
Lognormal Models to Life or Strength Data from Specimens of
Various Sizes", Nelson and Doganaksoy, NISTIR 4760, March 1992.
Applications:
Implementation Date:
Program:
LABEL CASE ASIS
X1LABEL X
YLIMITS 0 1
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 PNRCDF(X,10000) FOR X = 5 .05 5 AND
PLOT PNRCDF(X,3000) FOR X = 5 .05 5 AND
PLOT PNRCDF(X,1000) FOR X = 5 .05 5 AND
PLOT PNRCDF(X,300) FOR X = 5 .05 5 AND
PLOT PNRCDF(X,100) FOR X = 5 .05 5 AND
PLOT PNRCDF(X,50) FOR X = 5 .05 5 AND
PLOT PNRCDF(X,20) FOR X = 5 .05 5 AND
PLOT PNRCDF(X,5) FOR X = 5 .05 5 AND
PLOT PNRCDF(X,1) FOR X = 5 .05 5 AND
PLOT PNRCDF(X,0.5) FOR X = 5 .05 5 AND
PLOT PNRCDF(X,0.2) FOR X = 5 .05 5 AND
PLOT PNRCDF(X,0.1) FOR X = 5 .05 5
Date created: 11/13/2002
Last updated: 4/4/2003
Please email comments on this WWW page to
alan.heckert@nist.gov.
