Epstein test for exponentiality

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Description

Performs Epstein test for the composite hypothesis of exponentiality, see e.g. Ascher (1990).

Usage

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epstein.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:

EPS_n =\frac{2n≤ft(\log≤ft(n^{-1}∑_{i=1}^nD_i\right)-n^{-1}∑_{i=1}^n\log(D_i)\right)}{1+(n+1)/(6n)},

where D_i=(n-i+1)(X_{(i)}-X_{(i-1)}), X_{(0)}=0 and X_{(1)}≤q…≤q X_{(n)} are the order statistics. Under exponentiality, EPS is approximately distributed as a chi-square with n-1 degrees of freedom.

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 "Epstein test for exponentiality".

data.name

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

Author(s)

Alexey Novikov, Ruslan Pusev and Maxim Yakovlev

References

Ascher, S. (1990): A survey of tests for exponentiality. — Communications in Statistics – Theory and Methods, vol. 19, pp. 1811–1825.

Examples

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