IarcPEmid.int {pcds} | R Documentation |
The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - middle interval case
Description
Returns for points
and
, that is, returns 1 if
is in
, returns 0
otherwise, where
is the PE proximity region for point
and is constructed with expansion
parameter
and centrality parameter
for the interval
.
PE proximity regions are defined with respect to the middle interval int
and vertex regions are based
on the center associated with the centrality parameter . For the interval,
int
, the
parameterized center is
.
rv
is the index of the vertex region resides, with default=
NULL
.
If and
are distinct and either of them are outside interval
int
, it returns 0,
but if they are identical, then it returns 1 regardless of their locations
(i.e., loops are allowed in the digraph).
See also (Ceyhan (2012, 2016)).
Usage
IarcPEmid.int(p1, x2, int, r, c = 0.5, rv = NULL)
Arguments
p1 , x2 |
1D points; |
int |
A |
r |
A positive real number which serves as the expansion parameter in PE proximity region;
must be |
c |
A positive real number in |
rv |
The index of the vertex region |
Value
for points
and
that is, returns 1 if
is in
,
returns 0 otherwise
Author(s)
Elvan Ceyhan
References
Ceyhan E (2012).
“The Distribution of the Relative Arc Density of a Family of Interval Catch Digraph Based on Uniform Data.”
Metrika, 75(6), 761-793.
Ceyhan E (2016).
“Density of a Random Interval Catch Digraph Family and its Use for Testing Uniformity.”
REVSTAT, 14(4), 349-394.
See Also
IarcPEend.int
, IarcCSmid.int
, and IarcCSend.int
Examples
c<-.4
r<-2
a<-0; b<-10; int<-c(a,b)
IarcPEmid.int(7,5,int,r,c)
IarcPEmid.int(1,3,int,r,c)