B11PPF

B11PPF (LET)

Library Function

Compute the Burr type 11 percent point function with shape parameter r.

The standard Burr type 11 distribution has the following cumulative distribution function:

with r denoting the shape parameter.

The percent point function is computed by numerically inverting the cumulative distribution function.

This distribution can be extended with lower and upper bound parameters. If a and b denote the lower and upper bounds, respectively, then the location and scale parameters are:

location = a
scale = b - a


The general form of the distribution can then be found by using the relation

LET <y> = B11PPF(<p>,<r>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <p> is a number, parameter, or variable in the interval (0,1);
            <y> is a variable or a parameter (depending on what <p> is) where the computed Burr type 11 ppf 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 = B11PPF(0.95,0.2)
LET Y = B11PPF(P,0.5,0,5)
PLOT B11PPF(X,2,0,3) FOR X = 0.01 0.01 0.99

None

BURR TYPE XI is a synonym for BURR TYPE 11.

B11CDF	= Compute the Burr type 11 cumulative distribution function.
B11PDF	= Compute the Burr type 11 probability density 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.
BU9PDF	= Compute the Burr type 9 probability density function.
B10PDF	= Compute the Burr type 10 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 B11PPF(P,R) FOR X = 0.01  0.01  0.99
.
LET R  = 1
TITLE R = ^r
PLOT B11PPF(P,R) FOR X = 0.01  0.01  0.99
.
LET R  = 2
TITLE R = ^r
PLOT B11PPF(P,R) FOR X = 0.01  0.01  0.99
.
LET R  = 5
TITLE R = ^r
PLOT B11PPF(P,R) FOR X = 0.01  0.01  0.99
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Burr Type 11 Percent Point Functions