 Dataplot Vol 2 Vol 1

# DPUCDF

Name:
DPUCDF (LET)
Type:
Library Function
Purpose:
Compute the doubly Pareto uniform cumulative distribution function with shape parameters m and n, location parameter , and scale parameter ( - ).
Description:
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.

Syntax:
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.

Examples:
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
Default:
None
Synonyms:
None
Related Commands:
 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.
Reference:
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.

Applications:
Distributional Modeling
Implementation Date:
2007/10
Program:
```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
``` Date created: 1/8/2008
Last updated: 1/8/2008