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NCFPDFName:
follows a F distribution. If U is replaced with a non-central chi-square distribution with non-centrality parameter , then the above ratio follows a non-central F distribution with non-centrality parameter . The probability density function of the non-central F distribution is rather complicated and not given here. It is given on page 95 of Evans, Hastings, and Peacock (see the Reference section below). The input value and both degrees of freedom parameters should be positive and the non-centrality parameter should be non-negative ( = 0 reduces to the standard F distribution). The non-central F distribution can be generalized with location and scale parameters in the usual way.
<SUBSET/EXCEPT/FOR qualification> where <x> is a number, variable or a parameter containing non-negative values; <v1> is a non-negative number, parameter or variable that specifies the first degrees of freedom parameter; <v2> is a non-negative number, parameter or variable that specifies the second degrees of freedom parameter; <lambda> is a non-negative number, parameter or variable that specifies the non-centrality parameter; <loc> is a number or parameter that specifies the location parameter; <scale> is a number or parameter that specifies the scale parameter; <y> is a variable or a parameter (depending on what <y1> 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 = NCFPDF(2,10,10,5) LET X2 = NCFPDF(1.1,14,15,10000)
DATAPLOT computes the non-central F distribution by converting it to an equivalent non-central beta distribution. It then uses algorithm AS 226 (see the REFERENCE section below) obtained from the statlib archive to compute the non-central beta cdf. It uses the DBETAI and DLNGAM routines from the SLATEC library rather than the corresponding algorithms from the Applied Statistics series to compute the log gamma and incomplete beta functions.
LET NU2 = <value> LET LAMBDA = <value> LET Y = NON-CENTRAL F RANDOM NUMBERS FOR I = 1 1 N To generate a non-central F probability plot or an non-central F Kolmogorov-Smirnov or chi-square goodness of fit test, enter the following commands
LET NU2 = <value> LET LAMBDA = <value> NON-CENTRAL F PROBABILITY PLOT Y NON-CENTRAL F KOLMOGOROV SMIRNOV GOODNESS OF FIT Y NON-CENTRAL F CHI-SQUARE GOODNESS OF FIT Y
"Continuous Univariate Distributions: Volume 2", Johnson, Kotz, and Balakrishnan, Wiley and Sons, 1994, chapter 30. "Statistical Distributions", Third Edition, Evans, Hastings, and Peacock, 2000 pp. 95-97.
LABEL CASE ASIS Y1LABEL Probability X1LABEL X Y1LABEL DISPLACEMENT 12 X1LABEL DISPLACEMENT 12 TITLE DISPLACEMENT 2 Y1LIMITS 0 0.7 MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT SCALE FACTOR 2 MULTIPLOT 2 2 TITLE LAMBDA = 0 PLOT NCFPDF(X,10,5,0) FOR X = 0.01 0.01 5 TITLE LAMBDA = 0.5 PLOT NCFPDF(X,10,5,0.5) FOR X = 0.01 0.01 5 TITLE LAMBDA = 1 PLOT NCFPDF(X,10,5,1) FOR X = 0.01 0.01 5 TITLE LAMBDA = 2 PLOT NCFPDF(X,10,5,2) FOR X = 0.01 0.01 5 END OF MULTIPLOT CASE ASIS JUSTIFICATION CENTER MOVE 50 97 TEXT Non-Central F Distribution PDF (NU1 = 10, NU2 = 5)
Date created: 7/7/2004 |