BU9CDF

BU9CDF (LET)

Library Function

Compute the Burr type 9 cumulative distribution function with shape parameters r and k.

The Burr type 9 distribution is typically defined in terms of its cuumulative distribution function:

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 6 distribution.

LET <y> = BU9CDF(<x>,<r>,<k>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
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 9 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 A = BU9CDF(0.3,0.2,1.7)
LET Y = BU9CDF(X,0.5,2.2,0,5)
PLOT BU9CDF(X,2,1.8) FOR X = -5 0.01 5

None

BURR TYPE IX is a synonym for BURR TYPE 9.

BU9PDF	= Compute the Burr type 9 probability density function.
BU9PPF	= Compute the Burr type 9 percent point function.
BU2PDF	= Compute the Burr type 2 probability density function.
BU3PDF	= Compute the Burr type 3 probability density function.
BU4PDF	= Compute the Burr type 4 probability density function.
BU5PDF	= Compute the Burr type 5 probability density function.
BU6PDF	= Compute the Burr type 6 probability density function.
BU7PDF	= Compute the Burr type 7 probability density function.
BU8PDF	= Compute the Burr type 8 probability density function.
B10PDF	= Compute the Burr type 10 probability density function.
B11PDF	= Compute the Burr type 11 probability density function.
B12PDF	= Compute the Burr type 12 probability density function.
RAYPDF	= Compute the Rayleigh probability density function.
WEIPDF	= Compute the Weibull probability density function.
EWEPDF	= Compute the exponentiated Weibull probability density function.

Burr (1942), "Cumulative Frequency Functions", Annals of Mathematical Statistics, 13, pp. 215-232.

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.

Distributional Modeling

2007/10

 
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 BU9CDF(X,R,K) FOR X = -3  0.01  3
    END OF LOOP
END OF LOOP
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Burr Type 9 Cumulative Distribution Functions