BU2CDF

BU2CDF (LET)

Library Function

Compute the Burr type 2 cumulative distribution function with shape parameter r.

The Burr type 2 distribution is typically defined in terms of its cumulative distribution function:

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 2 distribution.

LET <y> = BU2CDF(<x>,<r>,<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 2 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 A = BU2CDF(0.3,0.2)
LET Y = BU2CDF(X,0.5,0,5)
PLOT BU2CDF(X,2,0,3) FOR X = 0 0.01 5

None

BURR TYPE II is a synonym for BURR TYPE 2.

BU2PDF	= Compute the Burr type 2 probability density function.
BU2PPF	= Compute the Burr type 2 percent point 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.
BU5PDF	= 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.
BU9PDF	= Compute the Burr type 9 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 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
.
LET R  = 0.5
TITLE R = ^r
PLOT BU2CDF(X,R) FOR X = 0.01  0.01  5
.
LET R  = 1
TITLE R = ^r
PLOT BU2CDF(X,R) FOR X = 0.01  0.01  5
.
LET R  = 2
TITLE R = ^r
PLOT BU2CDF(X,R) FOR X = 0.01  0.01  5
.
LET R  = 5
TITLE R = ^r
PLOT BU2CDF(X,R) FOR X = 0.01  0.01  5
.
END OF MULTIPLOT
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JUSTIFICATION CENTER
MOVE 50 97
TEXT Burr Type 2 Cumulative Distribution Functions