PEdom.num.norm.test: A test of segregation/association based on domination number...
In elvanceyhan/pcds: Proximity Catch Digraphs and Their Applications
PEdom.num.norm.test R Documentation
A test of segregation/association based on domination number of
Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data -
Normal Approximation
Description
An object of class "htest" (i.e., hypothesis test) function
which performs a hypothesis test of complete spatial
randomness (CSR) or uniformity of Xp points
in the convex hull of Yp points against the alternatives
of segregation (where Xp points cluster
away from Yp points i.e.,
cluster around the centers of the Delaunay
triangles) and association (where Xp points cluster
around Yp points) based on the normal approximation
to the binomial distribution of the domination number of PE-PCD
for uniform 2D data
in the convex hull of Yp points
The function yields the test statistic, p-value
for the corresponding alternative,
the confidence interval, estimate and null value
for the parameter of interest
(which is Pr(domination number\le 2)),
and method and name of the data set used.
Under the null hypothesis of uniformity of Xp points
in the convex hull of Yp points, probability of success
(i.e., Pr(domination number\le 2)) equals
to its expected value under the uniform distribution) and
alternative could be two-sided, or right-sided
(i.e., data is accumulated around the Yp points, or association)
or left-sided (i.e., data is accumulated
around the centers of the triangles,
or segregation).
PE proximity region is constructed
with the expansion parameter r \ge 1
and M-vertex regions where M
is a center that yields non-degenerate asymptotic distribution of
the domination number.
The test statistic is based on the normal approximation
to the binomial distribution,
when success is defined as domination number being less than
or equal to 2 in the one triangle case
(i.e., number of failures is equal to number of times
restricted domination number = 3
in the triangles).
That is, the test statistic is
based on the domination number for Xp points
inside convex hull of Yp
points for the PE-PCD and default convex hull correction, ch.cor,
is FALSE
where M is the center
that yields nondegenerate asymptotic distribution
for the domination number.
For this approximation to work,
number of Yp points must be at least 5
(i.e., about 7 or more Delaunay triangles)
and number of Xp points must be at least 7 times more than
the number of Yp points.
See also (\insertCiteceyhan:dom-num-NPE-Spat2011;textualpcds).
Usage
PEdom.num.norm.test(
Xp,
Yp,
r,
ch.cor = FALSE,
ndt = NULL,
alternative = c("two.sided", "less", "greater"),
conf.level = 0.95
)
Arguments
Xp
A set of 2D points
which constitute the vertices of the PE-PCD.
Yp
A set of 2D points
which constitute the vertices of the Delaunay triangles.
r
A positive real number
which serves as the expansion parameter in PE proximity region;
must be in (1,1.5].
ch.cor
A logical argument for convex hull correction,
default ch.cor=FALSE,
recommended when both Xp and Yp
have the same rectangular support.
ndt
Number of Delaunay triangles based on Yp points,
default is NULL.
alternative
Type of the alternative hypothesis in the test,
one of "two.sided", "less", "greater".
conf.level
Level of the confidence interval,
default is 0.95, for the domination number of
PE-PCD whose vertices are the 2D data set Xp.
Value
A list with the elements
statistic
Test statistic
p.value
The p-value for the hypothesis test
for the corresponding alternative
conf.int
Confidence interval for the domination number
at the given level conf.level and
depends on the type of alternative.
estimate
A vector with two entries:
first is the domination number,
and second is the estimate of the parameter, i.e.,
Pr(Domination Number=3)
null.value
Hypothesized value for the parameter,
i.e., the null value for expected domination number
alternative
Type of the alternative hypothesis in the test,
one of "two.sided", "less", "greater"
method
Description of the hypothesis test
data.name
Name of the data set
Author(s)
Elvan Ceyhan
References
\insertAllCited
See Also
PEdom.num.binom.test
Examples
## Not run:
nx<-100; ny<-5 #try also nx<-1000; ny<-10
r<-1.5 #try also r<-2 or r<-1.25
set.seed(1)
Xp<-cbind(runif(nx,0,1),runif(nx,0,1))
Yp<-cbind(runif(ny,0,.25),
runif(ny,0,.25))+cbind(c(0,0,0.5,1,1),c(0,1,.5,0,1))
#try also Yp<-cbind(runif(ny,0,1),runif(ny,0,1))
plotDelaunay.tri(Xp,Yp,xlab="",ylab="")
PEdom.num.norm.test(Xp,Yp,r) #try also PEdom.num.norm.test(Xp,Yp,r, alt="l")
PEdom.num.norm.test(Xp,Yp,1.25,ch=TRUE)
#or try
ndt<-num.delaunay.tri(Yp)
PEdom.num.norm.test(Xp,Yp,r,ndt=ndt)
#values might differ due to the random of choice of the three centers M1,M2,M3
#for the non-degenerate asymptotic distribution of the domination number
## End(Not run)
elvanceyhan/pcds documentation built on June 29, 2023, 8:12 a.m.
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| PEdom.num.norm.test | R Documentation |
A test of segregation/association based on domination number of Proportional Edge Proximity Catch Digraph (PE-PCD) for 2D data - Normal Approximation
Description
An object of class "htest" (i.e., hypothesis test) function
which performs a hypothesis test of complete spatial
randomness (CSR) or uniformity of Xp points
in the convex hull of Yp points against the alternatives
of segregation (where Xp points cluster
away from Yp points i.e.,
cluster around the centers of the Delaunay
triangles) and association (where Xp points cluster
around Yp points) based on the normal approximation
to the binomial distribution of the domination number of PE-PCD
for uniform 2D data
in the convex hull of Yp points
The function yields the test statistic, p-value
for the corresponding alternative,
the confidence interval, estimate and null value
for the parameter of interest
(which is Pr(domination number\le 2)),
and method and name of the data set used.
Under the null hypothesis of uniformity of Xp points
in the convex hull of Yp points, probability of success
(i.e., Pr(domination number\le 2)) equals
to its expected value under the uniform distribution) and
alternative could be two-sided, or right-sided
(i.e., data is accumulated around the Yp points, or association)
or left-sided (i.e., data is accumulated
around the centers of the triangles,
or segregation).
PE proximity region is constructed
with the expansion parameter r \ge 1
and M-vertex regions where M
is a center that yields non-degenerate asymptotic distribution of
the domination number.
The test statistic is based on the normal approximation
to the binomial distribution,
when success is defined as domination number being less than
or equal to 2 in the one triangle case
(i.e., number of failures is equal to number of times
restricted domination number = 3
in the triangles).
That is, the test statistic is
based on the domination number for Xp points
inside convex hull of Yp
points for the PE-PCD and default convex hull correction, ch.cor,
is FALSE
where M is the center
that yields nondegenerate asymptotic distribution
for the domination number.
For this approximation to work,
number of Yp points must be at least 5
(i.e., about 7 or more Delaunay triangles)
and number of Xp points must be at least 7 times more than
the number of Yp points.
See also (\insertCiteceyhan:dom-num-NPE-Spat2011;textualpcds).
Usage
PEdom.num.norm.test(
Xp,
Yp,
r,
ch.cor = FALSE,
ndt = NULL,
alternative = c("two.sided", "less", "greater"),
conf.level = 0.95
)
Arguments
Xp |
A set of 2D points which constitute the vertices of the PE-PCD. |
Yp |
A set of 2D points which constitute the vertices of the Delaunay triangles. |
r |
A positive real number
which serves as the expansion parameter in PE proximity region;
must be in |
ch.cor |
A logical argument for convex hull correction,
default |
ndt |
Number of Delaunay triangles based on |
alternative |
Type of the alternative hypothesis in the test,
one of |
conf.level |
Level of the confidence interval,
default is |
Value
A list with the elements
statistic |
Test statistic |
p.value |
The |
conf.int |
Confidence interval for the domination number
at the given level |
estimate |
A |
null.value |
Hypothesized value for the parameter, i.e., the null value for expected domination number |
alternative |
Type of the alternative hypothesis in the test,
one of |
method |
Description of the hypothesis test |
data.name |
Name of the data set |
Author(s)
Elvan Ceyhan
References
\insertAllCitedSee Also
PEdom.num.binom.test
Examples
## Not run:
nx<-100; ny<-5 #try also nx<-1000; ny<-10
r<-1.5 #try also r<-2 or r<-1.25
set.seed(1)
Xp<-cbind(runif(nx,0,1),runif(nx,0,1))
Yp<-cbind(runif(ny,0,.25),
runif(ny,0,.25))+cbind(c(0,0,0.5,1,1),c(0,1,.5,0,1))
#try also Yp<-cbind(runif(ny,0,1),runif(ny,0,1))
plotDelaunay.tri(Xp,Yp,xlab="",ylab="")
PEdom.num.norm.test(Xp,Yp,r) #try also PEdom.num.norm.test(Xp,Yp,r, alt="l")
PEdom.num.norm.test(Xp,Yp,1.25,ch=TRUE)
#or try
ndt<-num.delaunay.tri(Yp)
PEdom.num.norm.test(Xp,Yp,r,ndt=ndt)
#values might differ due to the random of choice of the three centers M1,M2,M3
#for the non-degenerate asymptotic distribution of the domination number
## End(Not run)
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