# deshpande.exp.test: Deshpande test for exponentiality In exptest: Tests for Exponentiality

## Description

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

## Usage

 1 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

 1 2 deshpande.exp.test(rexp(100)) deshpande.exp.test(rweibull(100,1.5)) 

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