 Dataplot Vol 2 Vol 1

# MAXPPF

Name:
MAXPPF (LET)
Type:
Library Function
Purpose:
Compute the Maxwell-Boltzman percent point function.
Description:
The standard Maxwell-Boltzman distribution has the following cumulative distribution function: with denoting the shape parameter and denoting the incomplete gamma function.

The percent point function is the inverse of the cumulative distribution function and the Maxwell-Boltzman percent point function is computed by numerically inverting the above cumulative distribution function.

If = 1, the Maxwell-Boltzman distribution is equivalent to the standard chi distribution with 3 degrees of freedom.

Note that is essentially a scale parameter. However, it is not strictly a scale parameter in the sense that the following relationship does not hold: The term would have to be for this relationship to hold (that is, there is an extra term).

The Maxwell-Boltzman distribution is sometimes parameterized using In scientific applications, the parameter is typically parameterized in a way that has physical meaning.

The Maxwell-Boltzman distribution can be generalized with location and scale parameters in the usual way. However, the scale parameter is not typically used since behaves much like a scale parameter already.

Syntax:
LET <y> = MAXPPF(<p>,<sigma>,<loc>,<scale>)
<SUBSET/EXCEPT/FOR qualification>
where <p> is a variable or a parameter;
<sigma> is an optional number or parameter that specifies the value of the shape parameter;
<loc> is an optional number or parameter that specifies the value of the location parameter;
<scale> is an optional positive number or parameter that specifies the value of the scale parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed Maxwell-Boltzman ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

If <sigma> is omitted, it defaults to 1. The location and scale parameters are optional.

Examples:
LET Y = MAXPPF(0.95)
LET Y = MAXPPF(0.95,0.3)
LET Y = MAXPPF(P1,SIGMA,MU)
PLOT MAXPPF(P,SIGMA) FOR P = 0 0.01 0.99
Default:
None
Synonyms:
None
Related Commands:
 MAXCDF = Compute the Maxwell cumulative distribution function. MAXPDF = Compute the Maxwell probability density function. CHPDF = Compute the chi probability density function. RAYPDF = Compute the Rayleigh probability density function. WEIPDF = Compute the Weibull probability density function. NORPDF = Compute the normal probability density function. LGNPDF = Compute the lognormal probability density function.
Reference:
"Continuous Univariate Distributions: Volume I", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, p. 451.
Applications:
Distributional Modeling, Statistical Physics
Implementation Date:
7/2004
Program:

Date created: 7/28/2004
Last updated: 7/28/2004