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UTSCDFName:
where
n1, n3, > 0 The case where a = 0 and d = 1 is referred to as the standard uneven two-sided power distribution. The a and d parameters are lower and upper limit parameters. These are related to location and scale parameters as follows
scale = d - a Kotz and Van Dorp show that the standard uneven two-sided power cumulative distribution can also be given as
where
0 ≤ ≤ 1 Kotz and Van Dorp use this form to derive some of the properties of this distribution.
The unveven two-sided power distribution is a generalization of the
two-sided power distribution. It is also
related to the (the center part of the generalized trapezoid
distribution shrinks to a single point). See Van Dorp and Kotz for
details.
The special case where
= 1 is referred
to as the generalized two-sided power distribution.
<SUBSET/EXCEPT/FOR qualification> where <x> is a variable, number, or parameter containing values in the interval (a,d); <a> is a number, parameter, or variable that specifies the first shape parameter; <b> is a number, parameter, or variable that specifies the second shape parameter; <d> is a number, parameter, or variable that specifies the third shape parameter; <n1> is a number, parameter, or variable that specifies the fourth shape parameter; <n3> is a number, parameter, or variable that specifies the fifth shape parameter; <alpha> is a number, parameter, or variable that specifies the sixth shape parameter; <y> is a variable or a parameter (depending on what <x> is) where the computed cdf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y = UTSCDF(X,0,0.8,1,2,2,0.5) LET Y = UTSCDF(X,A,B,D,N1,N3,ALPHA)
LABEL CASE ASIS TITLE CASE ASIS TITLE OFFSET 2 . MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT SCALE FACTOR 2 . MULTIPLOT 2 2 LET A = 0 LET B = 0.4 LET D = 1.0 LET N1 = 2 LET N3 = 0.5 LET A2 = A + 0.01 LET D2 = D - 0.01 . LET ALPHA = 0.5 TITLE N1 = ^n1, N3 = ^n3, Alpha = ^alpha PLOT UTSCDF(X,A,B,D,N1,N3,ALPHA) FOR X = A2 0.01 D2 . LET ALPHA = 1.0 TITLE N1 = ^n1, N3 = ^n3, Alpha = ^alpha PLOT UTSCDF(X,A,B,D,N1,N3,ALPHA) FOR X = A2 0.01 D2 . LET ALPHA = 2.0 TITLE N1 = ^n1, N3 = ^n3, Alpha = ^alpha PLOT UTSCDF(X,A,B,D,N1,N3,ALPHA) FOR X = A2 0.01 D2 . LET ALPHA = 5.0 TITLE N1 = ^n1, N3 = ^n3, Alpha = ^alpha PLOT UTSCDF(X,A,B,D,N1,N3,ALPHA) FOR X = A2 0.01 D2 . END OF MULTIPLOT . JUSTIFICATION CENTER MOVE 50 97 TEXT Uneven Two-Sided Power Cumulative Distribution Functions . MULTIPLOT 2 2 LET N1 = 0.5 LET N3 = 2 . LET ALPHA = 0.5 TITLE N1 = ^n1, N3 = ^n3, Alpha = ^alpha PLOT UTSCDF(X,A,B,D,N1,N3,ALPHA) FOR X = A2 0.01 D2 . LET ALPHA = 1.0 TITLE N1 = ^n1, N3 = ^n3, Alpha = ^alpha PLOT UTSCDF(X,A,B,D,N1,N3,ALPHA) FOR X = A2 0.01 D2 . LET ALPHA = 2.0 TITLE N1 = ^n1, N3 = ^n3, Alpha = ^alpha PLOT UTSCDF(X,A,B,D,N1,N3,ALPHA) FOR X = A2 0.01 D2 . LET ALPHA = 5.0 TITLE N1 = ^n1, N3 = ^n3, Alpha = ^alpha PLOT UTSCDF(X,A,B,D,N1,N3,ALPHA) FOR X = A2 0.01 D2 . END OF MULTIPLOT . JUSTIFICATION CENTER MOVE 50 97 TEXT Uneven Two-Sided Power Cumulative Distribution Functions . MULTIPLOT 2 2 LET N1 = 2 LET N3 = 2 . LET ALPHA = 0.5 TITLE N1 = ^n1, N3 = ^n3, Alpha = ^alpha PLOT UTSCDF(X,A,B,D,N1,N3,ALPHA) FOR X = A2 0.01 D2 . LET ALPHA = 1.0 TITLE N1 = ^n1, N3 = ^n3, Alpha = ^alpha PLOT UTSCDF(X,A,B,D,N1,N3,ALPHA) FOR X = A2 0.01 D2 . LET ALPHA = 2.0 TITLE N1 = ^n1, N3 = ^n3, Alpha = ^alpha PLOT UTSCDF(X,A,B,D,N1,N3,ALPHA) FOR X = A2 0.01 D2 . LET ALPHA = 5.0 TITLE N1 = ^n1, N3 = ^n3, Alpha = ^alpha PLOT UTSCDF(X,A,B,D,N1,N3,ALPHA) FOR X = A2 0.01 D2 . END OF MULTIPLOT . JUSTIFICATION CENTER MOVE 50 97 TEXT Uneven Two-Sided Power Cumulative Distribution Functions
Date created: 12/17/2007 |