The case where = 0 and = 1 is referred to as the standard Maxwell-Boltzman distribution.
The Maxwell-Boltzman distribution is equivalent to the chi distribution with 3 degrees of freedom.
The Maxwell-Boltzman distribution is sometimes parameterized using
In scientific applications, the parameter is typically parameterized in a way that has physical meaning.
where <x> is a variable or a parameter;
<loc> is an optional number or parameter that specifies the value of the location parameter;
<sigma> is an optional 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 pdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
If <loc> and <sigma> are omitted, they default to 0 and 1, respectively.
LET Y = MAXPDF(3,0,0.3)
LET Y = MAXPDF(X1,MU,SIGMA)
PLOT MAXPDF(X,0,SIGMA) FOR X = 0 0.01 5
MAXWELL PROBABILITY PLOT Y
MAXWELL PROBABILITY PLOT Y X
MAXWELL PROBABILITY PLOT Y XLOW XHIGH
MAXWELL KOLMOGOROV SMIRNOV GOODNESS OF FIT Y
MAXWELL CHI-SQUARE GOODNESS OF FIT Y X
MAXWELL CHI-SQUARE GOODNESS OF FIT Y XLOW XHIGH
You can use the probability plot to estimate and
LET SIGMA = PPA1
LET MU = PPA0
You can obtain a maximum likelihood estimate of with the command
This command will generate an estimate of using 0 as the estimate of location and an estimate of using the minimum of the data as an estimate of location. If the data minimum is negative, then both cases will use the data minimum as the estimate of location (i.e., the estimate of sigma will be the same). If you have a different estimate of locaiton, enter the command
before the MAXWELL MAXIMUM LIKELIHOOD command. This will be used in place of the data minimum estimate of location. Uncertainty estimates can be obtained using the DISTRIBUTIONAL BOOTSTRAP command
2/2008: Corrected to be a scale parameter rather than a shape parameter
Y1LABEL Probability X1LABEL X LABEL CASE ASIS TITLE CASE ASIS TITLE Maxwell Probability Density PLOT MAXPDF(X) FOR X = 0 0.01 5
Date created: 7/28/2004