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

1 | ```
deshpande.exp.test(x, b=0.44, simulate.p.value=FALSE, nrepl=2000)
``` |

`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. |

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)).

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. |

Alexey Novikov and Ruslan Pusev

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

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

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