| Type: | Package |
| Title: | Graph Theoretic Randomness Tests |
| Version: | 0.1.0 |
| Date: | 2025-08-28 |
| Description: | A collection of functions for testing randomness (or mutual independence) in linear and circular data as proposed in Gehlot and Laha (2025a) <doi:10.48550/arXiv.2506.21157> and Gehlot and Laha (2025b) <doi:10.48550/arXiv.2506.23522>, respectively. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Imports: | stats, circular |
| Suggests: | knitr, rmarkdown, timeSeriesDataSets |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2025-08-28 12:49:17 UTC; gehlo |
| Author: | Shriya Gehlot [aut, cre], Arnab Kumar Laha [aut] |
| Maintainer: | Shriya Gehlot <phd20shriyag@iima.ac.in> |
| Repository: | CRAN |
| Date/Publication: | 2025-09-02 21:10:20 UTC |
Theoretical CDF for RCAG for a given number of vertices.
Description
Computes the theoretical CDF for an RCAG with for a given number of vertices.
Usage
cdf.rcag(m)
Arguments
m |
Number of observations. |
Value
A vector representing the theoretical CDF of an RCAG with m/2 vertices.
Examples
cdf.rcag(1000)
Theoretical CDF of RIG for a given number of vertices.
Description
Computes the theoretical CDF for RIG with for a given number of vertices.
Usage
cdf.rig(m)
Arguments
m |
Number of observations. |
Value
A vector representing the theoretical CDF of RIG with m/2 vertices.
Examples
cdf.rig(1000)
Degree Calculation for Random Circular Graph
Description
Computes the degree of each vertex in a Random Circular Graph based on input arcs.
Usage
deg.rcag(theta)
Arguments
theta |
A numeric vector of length m=2*nv. |
Value
A vector of degrees for each vertex of RCAG obtained using theta.
Examples
x <- arima.sim(model = list(ar=0.9), 1000) ## AR(1) model
theta <- ((2*atan(x))%%(2*pi))*(180/pi) ##LAR(1) model
deg.rcag(theta)
Degree Calculation for Random Interval Graph
Description
Computes the degree of each vertex in a Random Interval Graph based on the input intervals.
Usage
deg.rig(x)
Arguments
x |
A numeric vector of length m=2*nv. |
Value
A vector of degrees for each vertex of RIG obtained using x.
Examples
x <- arima.sim(model = list(ar=0.7), 1000) ## AR(1) model
deg.rig(x)
Hellinger Distance Between Distributions
Description
Calculates the Hellinger distance between two probability distributions.
Usage
hellinger.dist(p, q)
Arguments
p |
A probability vector. |
q |
Another probability vector of same length as p. |
Value
Hellinger distance between p and q.
Proportion of Non-Intersecting Arc Pairs in an RCAG.
Description
Computes the proportion of non-intersecting pairs of arcs in the RCAG obtained using data.
Usage
nip.rcag(s, t, e1, e2)
Arguments
s |
Start points of arcs. |
t |
End points of arcs. |
e1 |
Vector of indices for the first interval in each pair. |
e2 |
Vector of indices for the second interval in each pair. |
Value
Mean proportion of non-intersecting pairs.
Examples
s <- circular::rcircularuniform(10)
t <- circular::rcircularuniform(10)
e1 <- c(2,10,6,1,5)
e2 <- c(4,3,8,7,9)
nip.rcag(s,t,e1,e2)
Proportion of Non-Intersecting Interval Pairs in an RIG
Description
Computes the proportion of non-intersecting pairs of interval in the RIG obtained using data.
Usage
nip.rig(s, t, e1, e2)
Arguments
s |
Start points of intervals. |
t |
End points of intervals. |
e1 |
Vector of indices for the first interval in each pair. |
e2 |
Vector of indices for the second interval in each pair. |
Value
Mean proportion of non-intersecting pairs.
Examples
s <- runif(10,0,1)
t <- runif(10,0,1)
e1 <- c(2,10,6,1,5)
e2 <- c(4,3,8,7,9)
nip.rig(s,t,e1,e2)
RCAG-DD Test
Description
Performs the RCAG-DD RIG-DD test of randomness for circular data.
Usage
rcagdd.test(theta)
Arguments
theta |
A numeric vector representing endpoints of arcs. |
Value
Vector of test statistics of RCAG-DD Test.
Examples
x <- arima.sim(model = list(ar=c(0.6,0.3)), 1000) ## AR(2) model
theta <- ((2*atan(x))%%(2*pi))*(180/pi) ##LAR(2) model
rcagdd.test(theta)
RCAG-EP Test
Description
Performs the RCAG-EP test of randomness for circular data.
Usage
rcagep.test(theta, alpha)
Arguments
theta |
A numeric vector. |
alpha |
The level of significance |
Value
Probability of non-intersection of edges, cutoff for RCAG-EP test and adjusted p-values for the RCAG-EP test.
Examples
x <- arima.sim(model = list(ar=0.9), 1000) ## AR(1) model
theta <- ((2*atan(x))%%(2*pi))*(180/pi) ##LAR(1) model
rcagep.test(theta,0.05)
RIG-DD Test
Description
Performs the RIG-DD test of randomness.
Usage
rigdd.test(x)
Arguments
x |
A numeric vector corresponding to interval of an RIG. |
Value
Vector of test statistics of RIG-DD Test.
Examples
x <- arima.sim(model = list(ar=c(0.7,0.2)), 1000) ## AR(2) model
rigdd.test(x)
RIG-EP Test
Description
Performs the RIG-EP test of randomness.
Usage
rigep.test(x, alpha)
Arguments
x |
A numeric vector |
alpha |
The level of significance |
Value
Probability of non-intersection of edges, cutoff for RIG-EP test and adjusted p-values for the RIG-EP test.
Examples
x <- arima.sim(model = list(ar=0.9), 1000) ## AR(1) model
rigep.test(x,0.05)
Threshold for RCAG-DD Test of randomness for circular data
Description
Calculates a threshold for RCAG-DD test using simulated data.
Usage
thrsd.rcagdd(m, n_iter, alpha)
Arguments
m |
Number of observations. |
n_iter |
Number of simulations. |
alpha |
Level of significance. |
Value
Threshold value for RCAG-DD test. thrsd.rcagdd(500,1000,0.05)
Threshold for RIG-DD Test of randomness
Description
Calculates a threshold for RIG-DD test using simulated data.
Usage
thrsd.rigdd(m, n_iter, alpha)
Arguments
m |
Number of observations. |
n_iter |
Number of simulation iterations. |
alpha |
Level of significance. |
Value
Threshold value for RIG-DD test.
Examples
thrsd.rigdd(250,1000,0.05)