exptest (version 1.2)

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

Description

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

Usage

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.

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.

Details

The test is based on the following statistic: $$I_n=\int_0^{\infty}(H_n(t)-G_n(t))dF_n(t),$$ where $F_n$ is the empirical distribution function, $$H_n(t) = \frac{1}{n^2}\sum_{i,j=1}^n 1{|X_i-X_j|

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

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