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NCBPDFName:
has a beta distribution with shape parameters A/2 and B/2. If is replaced with a non-central chi-square random variable, , with non-centrality parameter , then
has a non-central beta distribution with shape parameters A and B and non-centrality parameter . Dataplot computes the non-central beta probability density function by numerically integrating the non-central beta cumulative distribution function.
<SUBSET/EXCEPT/FOR qualification> where <x> is a number, parameter, or variable containing values between 0 and 1; <a> is a positive number, parameter, or variable that specifies the first shape parameter; <b> is a positive number, parameter, or variable that specifies the second shape parameter; <l> 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 = NCBPDF(A1,10,8,1.5) LET X2 = NCBPDF(X1,2,6,2)
Dataplot uses the DIFF routine from the Slatec library to compute the numerical derivative.
LET BETA = <value> LET LAMBDA = <value> LET Y = NON-CENTRAL BETA RANDOM NUMBERS FOR I = 1 1 N To generate an non-central beta probability plot or an non-central beta Kolmogorov-Smirnov or beta goodness of fit test, enter the following commands
LET BETA = <value> LET LAMBDA = <value> NON-CENTRAL BETA PROBABILITY PLOT Y NON-CENTRAL BETA KOLMOGOROV SMIRNOV ...
"Continuous Univariate Distributions--Volume II", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, pp. 502-504. "Statistical Distributions", Third Edition, Evans, Hastings, and Peacock, Wiley, 2000, chapter 5.
LABEL CASE ASIS Y1LABEL Probability X1LABEL X X1LABEL DISPLACEMENT 12 Y1LABEL DISPLACEMENT 12 TITLE DISPLACEMENT 2 Y1LIMITS 0 2 Y1TIC OFFSET 0 0.2 MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT SCALE FACTOR 2 MULTIPLOT 2 2 TITLE LAMBDA = 0 PLOT NCBPDF(X,2,4,0) FOR X = 0.01 0.01 0.99 TITLE LAMBDA = 1 PLOT NCBPDF(X,2,4,1) FOR X = 0.01 0.01 0.99 TITLE LAMBDA = 2 PLOT NCBPDF(X,2,4,2) FOR X = 0.01 0.01 0.99 TITLE LAMBDA = 5 PLOT NCBPDF(X,2,4,5) FOR X = 0.01 0.01 0.99 END OF MULTIPLOT CASE ASIS JUSTIFICATION CENTER MOVE 50 97 TEXT Non-Central Beta PDF (A = 2, B = 4)
Date created: 7/7/2004 |