# GoF tests based on the empirical characteristic function for the Exponential distribution

### Description

Computes the GoF tests based on the characteristic function of the Exponential distribution: Epps-Pulley (EP), Henze-Meintanis (W1, W2) and Meintanis-Iliopoulos test statistics (T1, T2).

### Usage

1 |

### Arguments

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

`type` |
the type of the test statistic used. "EP" is the default used test of Epps-Pulley,"W1" and "W2" for Henze and Meintanis, "T1" and "T2" for Meintanis-Iliopoulos test statistics. |

`a` |
parameter value to be adjusted for the test statistics ("W1", "W2", "T1" and "T2"). |

`nsim` |
an integer specifying the number of replicates used in Monte Carlo. |

### Details

The computation time of this function is quite long for the test statistics "W1", "W2", "T1" and "T2" because of their complex expression. The Monte-Carlo simulations take more time compared to the other tests. These tests are not defined for a=0.

### Value

An object of class htest.

### Author(s)

Meryam KRIT

### References

Epps T.W. and Pulley L.B., A test for exponentiality vs. monotone hazard alternatives derived from the empirical characteristic function, *Journal of the Royal Statistical Society, Series B*, 48, 206-213, 1986.

Henze N. and Meintanis S.G., Recent and classical tests for exponentiality: partial review with comparisons, *Metrika*, 61, 29-45, 2005.

Henze N. and Meintanis S.G., Goodness-of-fit tests based on a new characterization of the exponential distribution, *Communications in Statistics, Theory and Methods*, 31, 1479-1497, 2002.

Meintanis S.G. and Iliopoulos G., Characterizations of the exponential distribution based on certain properties of its characteristic function,
*Kybernetika*, 39 (3), 295-298, 2003.

### Examples

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