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:
statisticthe value of the test statistic.
p.valuethe p-value for the test.
methodthe character string "Deshpande test for exponentiality".
data.namea character string giving the name(s) of the data.
Details
The test is based on the following statistic:
$$J = \frac{1}{n(n - 1)}\, \sum_{i\ne j}1{x_i > bx_j}.$$
Under exponentiality, one has
$$\sqrt{n}(J-\frac{1}{b+1})\stackrel{d}{\rightarrow}\mathcal N\left(0,4\zeta_1\right),$$
where
$$\zeta_1 = \frac{1}{4}\left(1+\frac{b}{b+2}+\frac{1}{2b+1}+\frac{2(1-b)}{b+1}-\frac{2b}{b^2+b+1}-\frac{4}{(b+1)^2} \right)$$
(see Deshpande (1983)).
References
Deshpande J.V. (1983): A class of tests for exponentiality against increasing failure rate average alternatives. --- Biometrika, vol. 70, pp. 514--518.