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NCCPDFName:
follows a central chi-square distribution. This can be generalized with
That is, the normal random variable Ui has a location parameter i. The above sum follows a non-central chi-square distribution with non-centrality parameter
The probability density can be given as
with and denoting the shape parameters and Ia)(x) denoting the modified Bessel function of the first kind of order a. The non-central chi-square distribution is also referred to as the Rayleigh, Rayleigh-Rice, or Rice distribution in the literature.
<SUBSET/EXCEPT/FOR qualification> where <x> is a positive number, variable or a parameter; <v> is a positive number, parameter or variable that specifies the degrees of freedom parameter; <lambda> is a non-negative number, parameter or variable that specifies the non-centrality parameter; <loc> is a number, parameter or variable that specifies the location parameter; <scale> is a number, parameter or variable that specifies the scale parameter; <y> is a variable or a parameter (depending on what <x> is) where the computed pdf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional. Note that the location and scale parameters are optional.
LET A = NCCPDF(3,10,10)
LET LAMBDA = <value> LET Y = NON-CENTRAL CHI-SQUARE RANDOM NUMBERS ...
To generate an non-central chi-square probability plot or an non-central chi-square Kolmogorov-Smirnov or chi-square goodness of fit test, enter the following commands
LET LAMBDA = <value> NON-CENTRAL CHI-SQUARE PROBABILITY PLOT Y NON-CENTRAL CHI-SQUARE KOLMOGOROV SMIRNOV ...
To generate a PPCC or Kolmogorov-Smirnov plot, enter the following commands
LET NU2 = <value> LET LAMBDA1 = <value> LET LAMBDA2 = <value> NON-CENTRAL CHI-SQUARE PPCC PLOT Y NON-CENTRAL CHI-SQUARE KS PLOT Y The default values for NU1 and NU2 are 5 and 15. The default values for LAMBDA1 and LAMBDA2 are 0 and 10.
"Continuous Univariate Distributions--Volume 2", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 29. "Statistical Distributions", Third Edition, Evans, Hastings, and Peacock, 2000, chapter 9.
LABEL CASE ASIS Y1LABEL Probability X1LABEL X X1LABEL DISPLACEMENT 12 Y1LABEL DISPLACEMENT 12 YLIMITS 0 0.2 TITLE DISPLACEMENT 2 MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT SCALE FACTOR 2 MULTIPLOT 2 2 TITLE LAMBDA = 0 PLOT NCCPDF(X,5,0) FOR X = 0.01 0.01 10 TITLE LAMBDA = 0.5 PLOT NCCPDF(X,5,0.5) FOR X = 0.01 0.01 10 TITLE LAMBDA = 1 PLOT NCCPDF(X,5,1) FOR X = 0.01 0.01 10 TITLE LAMBDA = 2 PLOT NCCPDF(X,5,2) FOR X = 0.01 0.01 10 END OF MULTIPLOT CASE ASIS JUSTIFICATION CENTER MOVE 50 97 TEXT Non-Central Chi-Square PDF (NU = 5)
Date created: 7/7/2004 |