num.arcsCSmid.int {pcds} | R Documentation |
Returns the number of arcs of of Central Similarity Proximity Catch Digraphs (CS-PCDs) whose vertices are
the given 1D numerical data set, Xp
.
CS proximity region N_{CS}(x,t,c)
is defined with respect to the interval
int
=(a,b)
for this function. CS proximity region is constructed with expansion parameter t>0
and
centrality parameter c \in (0,1)
.
Vertex regions are based on the center associated with the centrality parameter c \in (0,1)
.
For the interval, int
=(a,b)
, the parameterized center is M_c=a+c(b-a)
and for the number of arcs,
loops are not allowed so arcs are only possible for points inside the middle interval int
for this function.
See also (Ceyhan (2016)).
num.arcsCSmid.int(Xp, int, t, c = 0.5)
Xp |
A set or |
int |
A |
t |
A positive real number which serves as the expansion parameter in CS proximity region. |
c |
A positive real number in |
Number of arcs for the CS-PCD whose vertices are the 1D data set, Xp
,
with expansion parameter, r \ge 1
, and centrality parameter, c \in (0,1)
. PE proximity regions are defined only
for Xp
points inside the interval int
, i.e., arcs are possible for such points only.
Elvan Ceyhan
Ceyhan E (2016). “Density of a Random Interval Catch Digraph Family and its Use for Testing Uniformity.” REVSTAT, 14(4), 349-394.
num.arcsCSend.int
, num.arcsPEmid.int
, and num.arcsPEend.int
c<-.4
t<-2
a<-0; b<-10; int<-c(a,b)
n<-10
Xp<-runif(n,a,b)
num.arcsCSmid.int(Xp,int,t,c)
num.arcsCSmid.int(Xp,int,t,c=.3)
num.arcsCSmid.int(Xp,int,t=1.5,c)
#num.arcsCSmid.int(Xp,int,t,c+5) #gives error
#num.arcsCSmid.int(Xp,int,t,c+10)
n<-10 #try also n<-20
Xp<-runif(n,a-5,b+5)
num.arcsCSint(Xp,int,t,c)
Xp<-runif(n,a+10,b+10)
num.arcsCSmid.int(Xp,int,t,c)
n<-10
Xp<-runif(n,a,b)
num.arcsCSmid.int(Xp,int,t,c)