PNRPPF

PNRPPF (LET)

Library Function

Compute the power-normal percent point function.

The standard power-normal distribution has the following percent point function:

where p is the shape (power) parameter and is the percent point function of the standard normal distribution. The input value is a real number between 0 and 1 (since it corresponds to a probability).

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

LET <y2> = PNRPPF(<y1>,<p>)        <SUBSET/EXCEPT/FOR qualification>
where <y1> is a number, parameter, or variable in the range 0 to 1;
              <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 ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = PNRPPF(0.9,2)
LET X2 = PNRPPF(X1,P)
LET X2 = PNRPPF(X1,0.5)

The general power-normal distribution has the following percent point function:

where and are the location and scale parameters, respectively.

None

None

PNRCDF	= Compute the power-normal cumulative density function.
PNRPDF	= Compute the power-normal probability density function.
PNRHAZ	= Compute the power-normal hazard function.
PNRCHAZ	= Compute the power-normal cumulative hazard function.
PLNPDF	= Compute the power-lognormal 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 Probabiulity 
Y1LABEL X 
YLIMITS -5 10 
TITLE CASE ASIS 
TITLE Power Normal PPF Plot CR() ... 
 SD=1, P=10000, 3000, 1000, 300, 100, 50, 20, 5, 1, 0.5, 0.2 0.1  
.  
PLOT PNRPPF(F,10000) FOR F = 0.01 0.01 0.99 AND  
PLOT PNRPPF(F,3000) FOR F = 0.01 0.01 0.99 AND  
PLOT PNRPPF(F,1000) FOR F = 0.01 0.01 0.99 AND  
PLOT PNRPPF(F,300) FOR F = 0.01 0.01 0.99 AND  
PLOT PNRPPF(F,100) FOR F = 0.01 0.01 0.99 AND  
PLOT PNRPPF(F,50) FOR F = 0.01 0.01 0.99 AND  
PLOT PNRPPF(F,20) FOR F = 0.01 0.01 0.99 AND  
PLOT PNRPPF(F,5) FOR F = 0.01 0.01 0.99 AND  
PLOT PNRPPF(F,1) FOR F = 0.01 0.01 0.99 AND  
PLOT PNRPPF(F,0.5) FOR F = 0.01 0.01 0.99 AND  
PLOT PNRPPF(F,0.2) FOR F = 0.01 0.01 0.99 AND  
PLOT PNRPPF(F,0.1) FOR F = 0.01 0.01 0.99