# tnl_Test

library(tnl.Test)

The goal of tnl.Test is to provide functions to perform the hypothesis tests for the two sample problem based on order statistics and power comparisons.

## Installation

You can install the released version of tnl.Test from CRAN with:

install.packages("tnl.Test")

Alternatively, you can install the development version on GitHub using the devtools package:

install.packages("devtools") # if you have not installed "devtools" package
devtools::install_github("ihababusaif/tnl.Test")

## Details

A non-parametric two-sample test is performed for testing null hypothesis $${H_0:F=G}$$ against the alternative hypothesis $${H_1:F\not=G}$$. The assumptions of the $${T_n^{(\ell)}}$$ 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 $${T_n^{(\ell)}}$$ 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 $${T_n^{(\ell)}}$$ 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 $${T_n^{(\ell)}}$$ test is also computed under Lehman alternative.
Random number generator of $${T_n^{(\ell)}}$$ test statistic are provided under null hypothesis in the library.

## Examples

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

library(tnl.Test)
require(stats)
x=rnorm(7,2,0.5)
y=rnorm(7,0,1)
tnl.test(x,y,l=2)
#> $statistic #> [1] 4 #> #>$p.value
#> [1] 0.1818182

ptnl gives the distribution function of $${T_n^{(\ell)}}$$ against the specified quantiles.

library(tnl.Test)
ptnl(q=2,n=6,m=9,l=2,exact="NULL")
#> $method #> [1] "exact" #> #>$cdf
#> [1] 0.01198801

dtnl gives the density of $${T_n^{(\ell)}}$$ against the specified quantiles.

library(tnl.Test)
dtnl(k=3,n=7,m=10,l=2,exact="TRUE")
#> $method #> [1] "exact" #> #>$pmf
#> [1] 0.02303579

qtnl gives the quantile function of $${T_n^{(\ell)}}$$ against the specified probabilities.

library(tnl.Test)
qtnl(p=c(.1,.3,.5,.8,1),n=8,m=8,l=1,exact="NULL",trial = 100000)
#> $method #> [1] "exact" #> #>$quantile
#> [1] 2 3 4 6 8

rtnl generates random values from $${T_n^{(\ell)}}$$.

library(tnl.Test)
rtnl(N=15,n=7,m=10,l=2)
#>  [1] 4 7 7 7 7 6 7 7 7 7 6 6 6 7 6

tnl_mean gives an expression for $$E({T_n^{(\ell)}})$$ under $${H_0:F=G}$$.

library(tnl.Test)
require(base)
tnl_mean(n.=11,m.=8, l=2)
#> [1] 7.016657

ptnl.lehmann gives the distribution function of $${T_n^{(\ell)}}$$ under Lehmann alternatives.

library(tnl.Test)
ptnl.lehmann(q=3, n.=7,m.=7,l = 2, gamma = 1.2)
#> [1] 0.09275172

dtnl.lehmann gives the density of $${T_n^{(\ell)}}$$ under Lehmann alternatives.

library(tnl.Test)
dtnl.lehmann(k=3, n.= 6,m.=8,l = 2, gamma = 0.8)
#> [1] 0.04111771

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

library(tnl.Test)
qtnl.lehmann(p=.3, n.=4,m.=7, l=1, gamma=0.5)
#> [1] 3

rtnl.lehmann generates random values from $${T_n^{(\ell)}}$$ under Lehmann alternatives.

library(tnl.Test)
rtnl.lehmann(N = 15, n. = 7,m.=10, l = 2,gamma=0.5)
#>  [1] 7 5 3 5 7 7 6 7 6 5 6 7 2 6 3

## Corresponding Author

Department of Statistics, Faculty of Science, Selcuk University, 42250, Konya, Turkey
www.researchgate.net/profile/Ihab-Abusaif
Email:

## References

Karakaya, K., Sert, S., Abusaif, I., Kuş, C., Ng, H. K. T., & Nagaraja, H. N. (2023). A Class of Non-parametric Tests for the Two-Sample Problem based on Order Statistics and Power Comparisons. Submitted paper.

Aliev, F., Özbek, L., Kaya, M. F., Kuş, C., Ng, H. K. T., & Nagaraja, H. N. (2022). A nonparametric test for the two-sample problem based on order statistics. Communications in Statistics-Theory and Methods, 1-25.