MCLCDF

MCLCDF (LET)

Library Function

Compute the McLeish cumulative distribution function.

The standard form of the McLeish distribution has the following probability density function:

with K(.) denoting the modified Bessel function of the of the second kind of order and denoting the gamma function.

The standard McLeish distribution can be generalized with location and scale parameters in the usual way.

The cumulative distribution function is computed by numerically integrating the probability density function. Dataplot performs the integration using the DQAG routine from the Slatec library.

LET <y> = MCLCDF(<x>,<alpha>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <x> is a variable, a number, or a parameter;
            <alpha> is a positive number of parameter that specifies the value of the shape parameter;
            <loc> is an optional number or parameter that specifies the value of the location parameter;
            <scale> is an optional positive number or parameter that specifies the value of the scale parameter;
            <y> is a variable or a parameter (depending on what <x> is) where the computed McLeish cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET Y = MCLCDF(3,1.5)
LET Y = MCLCDF(X1,ALPHA)
PLOT MCLCDF(X,ALPHA) FOR X = -10 0.01 10

DATAPLOT uses the routine BESK from the SLATEC Common Mathematical Library to compute the modified Bessel function of the third kind. SLATEC is a large set of high quality, portable, public domain Fortran routines for various mathematical capabilities maintained by seven federal laboratories.

None

None

MCLPDF	= Compute the McLeish probability density function.
MCLPPF	= Compute the McLeish percent point function.
GALPDF	= Compute the generalized asymmetric Laplace probability density function.
GIGPDF	= Compute the generalized inverse Gaussian probability density function.
BEIPDF	= Compute the Bessel I-function probability density function.
BEKPDF	= Compute the Bessel K-function probability density function.

Johnson, Kotz, and Balakrisnan, "Continuous Univariate Distributions--Volume I", Second Edition, Wiley, 1994, pp. 50-53.

Distributional Modeling

8/2004

 
Y1LABEL Probability
X1LABEL X
LABEL CASE ASIS
TITLE CASE ASIS
CASE ASIS
Y1LABEL DISPLACEMENT 12
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
TITLE Alpha = 1
PLOT MCLCDF(X,1) FOR X = -10  0.01 10
TITLE Alpha = 2
PLOT MCLCDF(X,2) FOR X = -10  0.01 10
TITLE Alpha = 5
PLOT MCLCDF(X,5) FOR X = -10  0.01 10
TITLE Alpha = 10
PLOT MCLCDF(X,10) FOR X = -10  0.01 10
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATION CENTER
TEXT McLeish Distribution