ahsanullah.exp.test: Test for exponentiality based on Ahsanullah characterization
In exptest: Tests for Exponentiality

Description Usage Arguments Details Value Author(s) References Examples

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

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

`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.

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)).

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.

Alexey Novikov and Ruslan Pusev

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.).

1 2	ahsanullah.exp.test(rexp(25)) ahsanullah.exp.test(rgamma(25,2))

	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