# rossberg.exp.test: Test for exponentiality based on Rossberg characterization In exptest: Tests for Exponentiality

## Description

Performs test for the composite hypothesis of exponentiality based on the Rossberg characterization, see Volkova (2010).

## Usage

 1 rossberg.exp.test(x) 

## Arguments

 x a numeric vector of data values.

## Details

The test is based on the following statistic:

S_n=\int_0^∞(H_n(t)-G_n(t))dF_n(t),

where F_n is the empirical distribution function,

H_n(t) = (C_n^3)^{-1}∑_{1≤q i<j<k≤q n}1\{X_{2,\{i,j,k\}}-X_{1,\{i,j,k\}}<t\}, \quad t≥q 0,

G_n(t) =(C_n^2)^{-1}∑_{1≤q i<j≤q n}1\{\min (X_i,X_j)<t\}, \quad t≥q 0.

Here X_{s,\{i,j,k\}}, s=1,2, denotes the sth order statistic of X_i,X_j,X_k. The p-value is computed from the limit null distribution. Under exponentiality, one has

√{n}S_n\stackrel{d}{\rightarrow}\mathcal N≤ft(0,\frac{52}{1125}\right)

(see, Volkova (2010)).

## 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 Rossberg characterization". data.name a character string giving the name(s) of the data.

## Author(s)

Ruslan Pusev and Maxim Yakovlev

## References

Volkova, K.Yu. (2010): On asymptotic efficiency of exponentiality tests based on Rossberg characterization. — J. Math. Sci., vol. 167, No. 4, pp. 486–494.

## Examples

 1 2 rossberg.exp.test(rexp(25)) rossberg.exp.test(runif(25, min = 50, max = 100)) 

### Example output

	Test for exponentiality based on Rossberg's characterization

data:  rexp(25)
Sn = 0.13103, p-value = 0.002309

Test for exponentiality based on Rossberg's characterization

data:  runif(25, min = 50, max = 100)
Sn = 0.34667, p-value = 6.661e-16


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