Deshpande test for exponentiality

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Description

Performs Deshpande test for the composite hypothesis of exponentiality, see Deshpande (1983).

Usage

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deshpande.exp.test(x, b=0.44, simulate.p.value=FALSE, nrepl=2000)

Arguments

x

a numeric vector of data values.

b

a parameter of the test (see below).

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:

J = \frac{1}{n(n - 1)}\, ∑_{i\ne j}1\{x_i > bx_j\}.

Under exponentiality, one has

√{n}(J-\frac{1}{b+1})\stackrel{d}{\rightarrow}\mathcal N≤ft(0,4ζ_1\right),

where

ζ_1 = \frac{1}{4}≤ft(1+\frac{b}{b+2}+\frac{1}{2b+1}+\frac{2(1-b)}{b+1}-\frac{2b}{b^2+b+1}-\frac{4}{(b+1)^2} \right)

(see Deshpande (1983)).

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 "Deshpande test for exponentiality".

data.name

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

Author(s)

Alexey Novikov and Ruslan Pusev

References

Deshpande J.V. (1983): A class of tests for exponentiality against increasing failure rate average alternatives. — Biometrika, vol. 70, pp. 514–518.

Examples

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