DPUCDF

DPUCDF (LET)

Library Function

Compute the doubly Pareto uniform cumulative distribution function with shape parameters m and n, location parameter , and scale parameter ( - ).

The doubly Pareto uniform distribution has the following cumulative distribution function:

with m and n denoting the shape parameters, denoting the location parameter, and ( - ) denoting the scale parameter.

This distribution is uniform between and . It has Paretian tails for both the lower and upper tails. The m parameter controls the shape of the lower tail and the n parameter controls the shape of the upper tail.

The case where = 0 and = 1 is referred to as the standard doubly Pareto uniform distribution.

LET <y> = DPUCDF(<x>,<m>,<n>,<alpha>,<beta>)
                        <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 double Pareto uniform cdf value is stored;
            <m> is a number, parameter, or variable that specifies the first shape parameter;
            <n> is a number, parameter, or variable that specifies the second shape paremeter;
            <alpha> is a number, parameter, or variable that specifies the location parameter;
            <beta> is a number, parameter, or variable (<beta> - <alpha> is the scale parameter);
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

If <alpha> and <beta> are omitted, they default to 0 and 1, respectively.

LET A = DPUCDF(0.3,1.4,3.2,0,1)
LET Y = DPUCDF(X,1.4,3.2,0,1)
PLOT DPUCDF(X,1.4,3.2,-5,5) FOR X = -10 0.1 10

None

None

DPUPDF	= Compute the doubly Pareto uniform probability density function.
DPUPPF	= Compute the doubly Pareto uniform percent point function.
TSPPDF	= Compute the two-sided power probability density function.
POWPDF	= Compute the power probability density function.
GTRPDF	= Compute the generalized trapezoid probability density function.
TSOPDF	= Compute the two-sided ogive probability density function.
OGIPDF	= Compute the ogive probability density function.
TSSPDF	= Compute the two-sided slope probability density function.
SLOPDF	= Compute the slope probability density function.
BETPDF	= Compute the Beta probability density function.
JSBPDF	= Compute the Johnson SB probability density function.

Singh, Van Dorp, Mazzuchi "A Novel Asymmetric Distribution with Power Tails", Communications in Statistics, Theory and Methods, Vol. 36 (2), to appear.

Van Dorp, Singh, and Mazzuchi "The Doubly-Pareto Uniform Distribution with Applications in Uncertainty Analysis and Econometrics", Mediterranean Journal of Mathematics, Vol. 3 (2), pp. 205-225.

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 ALPHA = 0
LET BETA  = 1
.
LET M = 0.5
LET N = 0.5
TITLE M = ^m, N = ^n
PLOT DPUCDF(X,M,N,ALPHA,BETA) FOR X = -5  0.01  5
.
LET M = 2
LET N = 0.5
TITLE M = ^m, N = ^n
PLOT DPUCDF(X,M,N,ALPHA,BETA) FOR X = -5  0.01  5
.
LET M = 0.5
LET N = 2
TITLE M = ^m, N = ^n
PLOT DPUCDF(X,M,N,ALPHA,BETA) FOR X = -5  0.01  5
.
LET M = 2
LET N = 2
TITLE M = ^m, N = ^n
PLOT DPUCDF(X,M,N,ALPHA,BETA) FOR X = -5  0.01  5
.
END OF MULTIPLOT
.
CASE ASIS
JUSTIFICATION CENTER
MOVE 50 97
TEXT Doubly Pareto Uniform Cumulative Distribution Functions