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.
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.
LET Y = MAXCDF(3,0.3)
LET Y = MAXCDF(X1,SIGMA,MU)
PLOT MAXCDF(X,SIGMA) FOR X = 0 0.01 5
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