Dataplot Vol 2 Vol 1

# MAXCDF

Name:
MAXCDF (LET)
Type:
Library Function
Purpose:
Compute the Maxwell-Boltzman cumulative distribution function.
Description:
The Maxwell-Boltzman distribution has the following cumulative distribution function:

with denoting the scale parameter and denoting the incomplete gamma 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> = MAXCDF(<x>,<sigma>,<loc>,<scale>)
<SUBSET/EXCEPT/FOR qualification>
where <x> 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 cdf 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 = MAXCDF(3)
LET Y = MAXCDF(3,0.3)
LET Y = MAXCDF(X1,SIGMA,MU)
PLOT MAXCDF(X,SIGMA) FOR X = 0 0.01 5
Default:
None
Synonyms:
None
Related Commands:
 MAXPDF = Compute the Maxwell probability density function. MAXPPF = Compute the Maxwell percent point 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:
```
Y1LABEL Probability
X1LABEL X
LABEL CASE ASIS
TITLE CASE ASIS
TITLE Maxwell Cumulative Distribution
PLOT MAXCDF(X,1) FOR X = 0  0.01  5
```

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