ahsanullah.exp.test: Test for exponentiality based on Ahsanullah characterization

Description Usage Arguments Details Value Author(s) References Examples

View source: R/ahsanullah.exp.test.R

Description

Performs test for the composite hypothesis of exponentiality based on the Ahsanullah characterization, see Volkova and Nikitin (2013).

Usage

1
ahsanullah.exp.test(x, simulate.p.value=FALSE, nrepl=2000)

Arguments

x

a numeric vector of data values.

simulate.p.value

a logical value indicating whether to compute p-values by Monte Carlo simulation.

nrepl

the number of replications in Monte Carlo simulation.

Details

The test is based on the following statistic:

I_n=\int_0^{∞}(H_n(t)-G_n(t))dF_n(t),

where F_n is the empirical distribution function,

H_n(t) = \frac{1}{n^2}∑_{i,j=1}^n 1\{|X_i-X_j|<t\}, \quad t≥q 0,

G_n(t) = \frac{1}{n^2}∑_{i,j=1}^n 1\{2\min (X_i,X_j)<t\}, \quad t≥q 0.

Under exponentiality, one has

√{n}I_n\stackrel{d}{\rightarrow}\mathcal N≤ft(0,\frac{647}{4725}\right)

(see Volkova and Nikitin (2013)).

Value

A list with class "htest" containing the following components:

statistic

the value of the test statistic.

p.value

the p-value for the test.

method

the character string "Test for exponentiality based on Ahsanullah characterization".

data.name

a character string giving the name(s) of the data.

Author(s)

Alexey Novikov and Ruslan Pusev

References

Volkova K. Yu., Nikitin Ya. Yu. (2013): Exponentiality tests based on Ahsanullah's characterization and their efficiency. — Zap. Nauchn. Sem. POMI, vol. 412, pp. 69–87 (in Russian); to be transl. in J. Math. Sci. (N.Y.).

Examples

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Example output

	Test for exponentiality based on Ahsanullah's characterization

data:  rexp(25)
In = 0.23718, p-value = 0.001351


	Test for exponentiality based on Ahsanullah's characterization

data:  rgamma(25, 2)
In = 0.24557, p-value = 0.0009063

exptest documentation built on May 1, 2019, 8:01 p.m.