tnl.test {tnl.Test} | R Documentation |
Non-parametric tests for the two-sample problem based on order statistics and power comparisons
Description
tnl.test
performs a nonparametric test for
two sample test on vectors of data.
ptnl
gives the distribution function of
against the specified quantiles.
dtnl
gives the density of
against the specified quantiles.
qtnl
gives the quantile function of
against the specified probabilities.
rtnl
generates random values from
.
tnl_mean()
gives an expression for
under
.
ptnl.lehmann
gives the distribution function of
under Lehmann alternatives.
dtnl.lehmann
gives the density of
under Lehmann alternatives.
qtnl.lehmann
gives the quantile function of
against the specified probabilities under
Lehmann alternatives.
rtnl.lehmann
generates random values from
under Lehmann alternatives.
Usage
tnl.test(x, y, l, exact = "NULL")
ptnl(q, n, m, l, exact = "NULL", trial = 1e+05)
dtnl(k, n, m, l, exact = "NULL", trial = 1e+05)
qtnl(p, n, m, l, exact = "NULL", trial = 1e+05)
rtnl(N, n, m, l)
tnl_mean(n., m., l)
ptnl.lehmann(q, n., m., l, gamma)
dtnl.lehmann(k, n., m., l, gamma)
qtnl.lehmann(p, n., m., l, gamma)
rtnl.lehmann(N, n., m., 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 |
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 , m |
samples 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. |
n. , m. |
samples size. |
gamma |
parameter of Lehmann alternative. |
Details
A non-parametric two-sample test is performed for testing null
hypothesis against the alternative
hypothesis
.
The assumptions of the
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 and
.
Exact and simulated p-values are available for the 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
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
test is also computed under Lehman alternative.
Random number generator of
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
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
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 .
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., 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.
Examples
require(stats)
x <- rnorm(7, 2, 0.5)
y <- rnorm(5, 0, 1)
tnl.test(x, y, l = 2)
ptnl(q = c(2, 5), n = 6, m = 5, l = 2, trial = 100000)
dtnl(k = c(1, 3, 6), n = 7, m = 5, l = 2)
qtnl(p = c(.3, .9), n = 4, m = 5, l = 1)
rtnl(N = 20, n = 7, m = 10, l = 1)
require(base)
tnl_mean(n. = 11, m. = 8, l = 1)
ptnl.lehmann(q = 3, n. = 5, m. = 7, l = 2, gamma = 1.2)
dtnl.lehmann(k = 3, n. = 6, m. = 5, l = 2, gamma = 0.8)
qtnl.lehmann(p = c(.1, .5, .9), n. = 7, m. = 5, l = 1, gamma = 0.5)
rtnl.lehmann(N = 15, n = 7,m=7, l = 2, gamma = 0.5)