tnl.test: Non-parametric tests for the two-sample problem based on...

In ihababusaif/tnlTEST: Non-Parametric Tests for the Two-Sample Problem

Description

tnl.test performs a nonparametric test for two sample test on vectors of data.

ptnl gives the distribution function of T_n^(ℓ) against the specified quantiles.

dtnl gives the density of T_n^(ℓ) against the specified quantiles.

qtnl gives the quantile function of T_n^(ℓ) against the specified probabilities.

rtnl generates random values from T_n^(ℓ).

tnl_mean gives an expression for E(T_n^(ℓ)) under H₀:F=G.

ptnl.lehmann gives the distribution function of T_n^(ℓ) under Lehmann alternatives.

dtnl.lehmann gives the density of T_n^(ℓ) under Lehmann alternatives.

qtnl.lehmann gives the quantile function of T_n^(ℓ) against the specified probabilities under Lehmann alternatives.

rtnl.lehmann generates random values from T_n^(ℓ) under Lehmann alternatives.

Usage

tnl.test(x, y, l, exact = "NULL")

ptnl(q, n, l, exact = "NULL", trial = 1e+05)

dtnl(k, n, l, exact = "NULL", trial = 1e+05)

qtnl(p, n, l, exact = "NULL", trial = 1e+05)

rtnl(N, n, l)

tnl_mean(n, l)

ptnl.lehmann(q, n, l, gamma)

dtnl.lehmann(k, n, l, gamma)

qtnl.lehmann(p, n, l, gamma)

rtnl.lehmann(N, n, l, gamma)

Arguments

x	the first (non-empty) numeric vector of data values.
y	the second (non-empty) numeric vector of data values.
l	class parameter of Tn(ℓ).
exact	the method that will be used. "NULL" or a logical indicating whether an exact should be computed. See ‘Details’ for the meaning of NULL.
n	sample size.
trial	number of trials for simulation.
k, q	vector of quantiles.
p	vector of probabilities.
N	number of observations. If length(N) > 1, the length is taken to be the number required.
gamma	parameter of Lehmann alternative.

Details

A non-parametric two-sample test is performed for testing null hypothesis H₀:F=G against the alternative hypothesis H₁:F ≠ G. The assumptions of the T_n^(ℓ) test are that both samples should come from a continuous distribution and the samples should have the same sample size.
Missing values are silently omitted from x and y.
Exact and simulated p-values are available for the T_n^(ℓ) test. If exact ="NULL" (the default) the p-value is computed based on exact distribution when the sample size is less than 11. Otherwise, p-value is computed based on a Monte Carlo simulation. If exact ="TRUE", an exact p-value is computed. If exact="FALSE" , a Monte Carlo simulation is performed to compute the p-value. It is recommended to calculate the p-value by a Monte Carlo simulation (use exact="FALSE"), as it takes too long to calculate the exact p-value when the sample size is greater than 10.
The probability mass function (pmf), cumulative density function (cdf) and quantile function of T_n^(ℓ) are also available in this package, and the above-mentioned conditions about exact ="NULL", exact ="TRUE" and exact="FALSE" is also valid for these functions.
Exact distribution of T_n^(ℓ) test is also computed under Lehman alternative.
Random number generator of T_n^(ℓ) test statistic are provided under null hypothesis in the library.

Value

tnl.test returns a list with the following components

statistic:

the value of the test statistic.

p.value:

the p-value of the test.

ptnl returns a list with the following components

method:

The method that was used (exact or simulation). See ‘Details’.

cdf:

distribution function of T_n^(ℓ) against the specified quantiles.

dtnl returns a list with the following components

method:

The method that was used (exact or simulation). See ‘Details’.

pmf:

density of T_n^(ℓ) against the specified quantiles.

qtnl returns a list with the following components

method:

The method that was used (exact or simulation). See ‘Details’.

quantile:

quantile function against the specified probabilities.

rtnl return N of the generated random values.

tnl_mean return the mean of T_n^(ℓ).

ptnl.lehmann return vector of the distribution under Lehmann alternatives against the specified gamma.

dtnl.lehmann return vector of the density under Lehmann alternatives against the specified gamma.

qtnl.lehmann returns a quantile function against the specified probabilities under Lehmann alternatives.

rtnl.lehmann return N of the generated random values under Lehmann alternatives.

References

Karakaya K. et al. (2021). A Class of Non-parametric Tests for the Two-Sample Problem based on Order Statistics and Power Comparisons . Submitted paper.
Aliev F. et al. (2021). A Nonparametric Test for the Two-Sample Problem based on Order Statistics. Submitted paper.

Examples

require(stats)
x <- rnorm(7, 2, 0.5)
y <- rnorm(7, 0, 1)
tnl.test(x, y, l = 2)
# $statistic
# [1] 2
#
# $p.value
# [1] 0.02447552
##############
ptnl(q = 2, n = 6, l = 2, trial = 100000)
# $method
# [1] "exact"
#
# $cdf
# [1] 0.03030303
##############
dtnl(k = 3, n = 7, l = 2)
# $method
# [1] "exact"
#
# $pmf
# [1] 0.05710956
## Not run: 
qtnl(p = .3, n = 4, l = 1, exact = "FALSE")
# $method
# [1] "Monte Carlo simulation"
#
# $quantile
# [1] 2

## End(Not run)
##############
rtnl(N = 15, n = 7, l = 2)
# [1] 7 5 5 6 7 5 4 7 7 6 7 3 6 3 5
##############
require(base)
tnl_mean(n = 11, l = 2)
# [1] 8.058115
##############
ptnl.lehmann(q = 3, n = 5, l = 2, gamma = 1.2)
# [1] 0.1529147
##############
dtnl.lehmann(k = 3, n = 6, l = 2, gamma = 0.8)
# [1] 0.08230829
qtnl.lehmann(p = .3, n = 4, l = 1, gamma = 0.5)
# [1] 2
##############
rtnl.lehmann(N = 15, n = 7, l = 2, gamma = 0.5)
# [1] 7 6 7 7 7 6 7 5 3 7 5 3 5 4 7

ihababusaif/tnlTEST documentation built on Dec. 20, 2021, 6:55 p.m.