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MAXPPFName:
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.
<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.
LET Y = MAXPPF(0.95,0.3) LET Y = MAXPPF(P1,SIGMA,MU) PLOT MAXPPF(P,SIGMA) FOR P = 0 0.01 0.99
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
Date created: 7/28/2004 |