with r, l, and s denoting the shape, location, and scale parameters, respectively.
The case where l = 0 and s = 1 is referred to as the standard Burr type 10 distribution.
If r = 1, the Burr type 10 distribution is equivalent to the Rayleigh distribution. For this reason, the Burr type 10 distribution is also referred to as the generalized Rayleigh distribution. It has found use in reliability applications.
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 10 cdf value is stored;
<r> is a positive number, parameter, or variable that specifies the 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 = B10CDF(X,0.5,0,5)
PLOT B10CDF(X,2,0,3) FOR X = 0 0.01 5
Raqab and Kundu (2006), "Burr Type X Distributions: Revisited", Journal of Probability and Statistical Sciences, Vol. 4, No. 2, pp. 179-193.
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 2 2 MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT SCALE FACTOR 2 . LET R = 0.5 TITLE R = ^r PLOT B10CDF(X,R) FOR X = 0.01 0.01 5 . LET R = 1 TITLE R = ^r PLOT B10CDF(X,R) FOR X = 0.01 0.01 5 . LET R = 2 TITLE R = ^r PLOT B10CDF(X,R) FOR X = 0.01 0.01 5 . LET R = 5 TITLE R = ^r PLOT B10CDF(X,R) FOR X = 0.01 0.01 5 . END OF MULTIPLOT . JUSTIFICATION CENTER MOVE 50 97 TEXT Burr Type 10 Cumulative Distribution Functions
Date created: 11/27/2007