PLNPDF

PLNPDF (LET)

Library Function

Compute the standard power-lognormal probability density function.

The standard power-lognormal distribution has the following probability density function:

where is a shape parameter, p is a 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 lognormal distribution.

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.

LET A = PLNPDF(3,2,1)
LET X2 = PLNPDF(X1,POW,SD)
LET X2 = PLNPDF(X1,0.5,0.5)

The general power-lognormal probability density function can be expressed in terms of the standard power-lognormal probability density function as follows:

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

None

None

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.

"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 
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