
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 MaxwellBoltzman percent point function is computed by numerically inverting the above cumulative distribution function. If = 1, the MaxwellBoltzman 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 MaxwellBoltzman distribution is sometimes parameterized using
In scientific applications, the parameter is typically parameterized in a way that has physical meaning. The MaxwellBoltzman 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 MaxwellBoltzman 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 