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Dataplot Vol 2 Vol 1

PLNPDF

Name:
    PLNPDF (LET)
Type:
    Library Function
Purpose:
    Compute the standard power-lognormal probability density function.
Description:
    The standard power-lognormal distribution has the following probability density function:

      f(x,sigma,p)=(p/(x*sigma))*NORPDF(ln(x)/sigma)*
NORCDF(-ln(x)/sigma)**(p-1)   for x, p, sigma > 0

    where sigma is a shape parameter, p is a shape (power) parameter, and NORCDF and NORPDF 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 lognormal distribution.

Syntax:
    LET <y> = PLNPDF(<x>,<p>,<s>)        <SUBSET/EXCEPT/FOR qualification>
    where <x> is a non-negative number, parameter, or variable;
                  <p> is a positive number, parameter, or variable that specifies the power parameter;
                  <s> is an optional positive number, parameter, or variable that specifies the shape parameter;
                  <y> is a variable or a parameter (depending on what <y1> is) where the computed power-lognormal pdf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    If the <s> parameter is omitted, it defaults to 1.

Examples:
    LET A = PLNPDF(3,2,1)
    LET X2 = PLNPDF(X1,POW,SD)
    LET X2 = PLNPDF(X1,0.5,0.5)
Note:
    The general power-lognormal probability density function can be expressed in terms of the standard power-lognormal probability density function as follows:

      f(x,sigma,p,loc,scale)=f((x-loc)/scale,sigma,p)/scale
 for x > loc,  sigma, p, scale > 0

    where loc and scale are the location and scales parameters, respectively.

Default:
    None
Synonyms:
    None
Related Commands:
    PLNCDF = Compute the power-lognormal cumulative distribution function.
    PLNPPF = Compute the power-lognormal percent point function.
    PLNHAZ = Compute the power-lognormal hazard function.
    PLNCHAZ = Compute the power-lognormal cumulative hazard function.
    PNRPDF = Compute the power-normal probability density function.
    LGNPDF = Compute the lognormal probability density function.
    HFNPDF = Compute the half-normal probability density function.
    NORPDF = Compute the normal probability density function.
Reference:
    "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.
Applications:
    Reliability
Implementation Date:
    1995/5
Program:
    LABEL CASE ASIS 
    X1LABEL X 
    Y1LABEL Probability 
    TITLE CASE ASIS 
    .  
    MULTIPLOT 2 2 
    MULTIPLOT CORNER COORDINATES 0 0 100 95 
    . 
    TITLE P = 0.5, SIGMA = 0.2, 0.4, 0.7, 1.0 
    PLOT PLNPDF(X,0.5,0.2) FOR X = 0.01 .01 3 AND 
    PLOT PLNPDF(X,0.5,0.4) FOR X = 0.01 .01 3 AND 
    PLOT PLNPDF(X,0.5,0.7) FOR X = 0.01 .01 3 AND 
    PLOT PLNPDF(X,0.5,1.0) FOR X = 0.01 .01 3 
    TITLE P = 1.0, SIGMA = 0.2, 0.4, 0.7, 1.0 
    PLOT PLNPDF(X,1.0,0.2) FOR X = 0.01 .01 3 AND 
    PLOT PLNPDF(X,1.0,0.4) FOR X = 0.01 .01 3 AND 
    PLOT PLNPDF(X,1.0,0.7) FOR X = 0.01 .01 3 AND 
    PLOT PLNPDF(X,1.0,1.0) FOR X = 0.01 .01 3 
    TITLE P = 5.0, SIGMA = 0.2, 0.4, 0.7, 1.0 
    PLOT PLNPDF(X,5.0,0.2) FOR X = 0.01 .01 2 AND 
    PLOT PLNPDF(X,5.0,0.4) FOR X = 0.01 .01 2 AND 
    PLOT PLNPDF(X,5.0,0.7) FOR X = 0.01 .01 2 AND 
    PLOT PLNPDF(X,5.0,1.0) FOR X = 0.01 .01 2 
    TITLE P = 20, SIGMA = 0.2, 0.4, 0.7, 1.0 
    PLOT PLNPDF(X,20,0.2) FOR X = 0.01 .01 1 AND 
    PLOT PLNPDF(X,20,0.4) FOR X = 0.01 .01 1 AND 
    PLOT PLNPDF(X,20,0.7) FOR X = 0.01 .01 1 AND 
    PLOT PLNPDF(X,20,1.0) FOR X = 0.01 .01 1 
    . 
    END OF MULTIPLOT 
    MOVE 50 97 
    JUSTIFICATION CENTER 
    TEXT Power Lognormal PDF's 
        
    plot generated by sample program

Date created: 11/13/2002
Last updated: 4/4/2003
Please email comments on this WWW page to alan.heckert@nist.gov.