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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:

      F(x;sigma)=2*GAMMAI(3/2,0.5*(1/sigma**2)*x**2)/SQRT(PI)  x >= 0; sigma > 0

    with sigma denoting the shape parameter and GAMMAI 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 sigma = 1, the Maxwell-Boltzman distribution is equivalent to the standard chi distribution with 3 degrees of freedom.

    Note that sigma is essentially a scale parameter. However, it is not strictly a scale parameter in the sense that the following relationship does not hold:

      f(x;scale) = (1/scale)*f(x/scale;1)

    The (1/sigma^2)^(3/2) term would have to be 1/sigma^2 for this relationship to hold (that is, there is an extra SQRT(1/sigma^2) term).

    The Maxwell-Boltzman distribution is sometimes parameterized using

      a

      In scientific applications, the sigma 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 sigma 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:
     
    X1LABEL Probability
    Y1LABEL X
    LABEL CASE ASIS
    TITLE CASE ASIS
    TITLE Maxwell Percent Point
    PLOT MAXPPF(P,1) FOR P = 0  0.01  0.99
        
    plot generated by sample program

Date created: 7/28/2004
Last updated: 7/28/2004
Please email comments on this WWW page to alan.heckert@nist.gov.