with r, k, l, and s denoting the two shape parameters, the location parameter, and the scale parameter, respectively.
The case where l = 0 and s = 1 is referred to as the standard Burr type 3 distribution.
If X has a Burr type 12 distribution, then 1/X has a Burr type 3 distribution. For this reason, the Burr type 3 distribution is often referred to as the inverse Burr distribution.
The Burr type 3 distribution is also sometimes referred to as the Dagum type I distribution.
where <x> is a number, parameter, or variable;
<y> is a variable or a parameter (depending on what <x> is) where the computed Burr type 3 cdf value is stored;
<r> is a positive number, parameter, or variable that specifies the first shape parameter;
<k> is a positive number, parameter, or variable that specifies the second shape parameter;
<loc> is a number, parameter, or variable that specifies the location parameter;
<scale> is a positive number, parameter, or variable that specifies the scale parameter;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
If <loc> and <scale> are omitted, they default to 0 and 1, respectively.
LET Y = BU3CDF(X,0.5,2,2,0,5)
PLOT BU3CDF(X,2,0,3) FOR X = 0 0.01 5
Johnson, Kotz, and Balakrishnan (1994), "Contiunuous Univariate Distributions--Volume 1", Second Edition, Wiley, pp. 53-54.
Devroye (1986), "Non-Uniform Random Variate Generation", Springer-Verlang, pp. 476-477.
LABEL CASE ASIS TITLE CASE ASIS TITLE OFFSET 2 . MULTIPLOT 4 4 MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT SCALE FACTOR 4 . LET RVAL = DATA 0.5 1 2 5 LET KVAL = DATA 0.5 1 2 5 . LOOP FOR IROW = 1 1 4 LOOP FOR ICOL = 1 1 4 LET R = RVAL(IROW) LET K = KVAL(ICOL) TITLE R = ^r, K = ^k PLOT BU3CDF(X,R,K) FOR X = 0.01 0.01 5 END OF LOOP END OF LOOP . END OF MULTIPLOT . JUSTIFICATION CENTER MOVE 50 97 TEXT Burr Type 3 Cumulative Distribution Functions
Date created: 11/27/2007