Description Usage Arguments Details Value Author(s) References Examples

View source: R/ahsanullah.exp.test.R

Performs test for the composite hypothesis of exponentiality based on the Ahsanullah characterization, see Volkova and Nikitin (2013).

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

`x` |
a numeric vector of data values. |

`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:

*
I_n=\int_0^{∞}(H_n(t)-G_n(t))dF_n(t),
*

where *F_n* is the empirical distribution function,

*
H_n(t) = \frac{1}{n^2}∑_{i,j=1}^n 1\{|X_i-X_j|<t\}, \quad t≥q 0,
*

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

Under exponentiality, one has

*
√{n}I_n\stackrel{d}{\rightarrow}\mathcal N≤ft(0,\frac{647}{4725}\right)
*

(see Volkova and Nikitin (2013)).

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 Ahsanullah characterization". |

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

Alexey Novikov and Ruslan Pusev

Volkova K. Yu., Nikitin Ya. Yu. (2013): Exponentiality tests based on Ahsanullah's characterization and their efficiency. — Zap. Nauchn. Sem. POMI, vol. 412, pp. 69–87 (in Russian); to be transl. in J. Math. Sci. (N.Y.).

1 2 | ```
ahsanullah.exp.test(rexp(25))
ahsanullah.exp.test(rgamma(25,2))
``` |

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