Description Usage Arguments Details Value References See Also Examples

Supremum class version of the Upper Tail Anderson-Darling test providing a comparison of a fitted distribution with the empirical distribution.

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`x` |
a numeric vector of data values |

`distn` |
character string naming the null distribution |

`fit` |
list of null distribution parameters |

`H` |
a treshold value |

`alternative` |
indicates the alternative hypothesis and must be one of "two.sided" (default), "less", or "greater". Initial letter must be specified only. |

`sim` |
maximum number of szenarios in the Monte-Carlo simulation |

`tol` |
if the difference of two subsequent p-value calculations is lower than |

`estfun` |
an function as character string or |

The supremum class Upper Tail Anderson-Darling test compares the null distribution with the empirical distribution function of the observed data. The test statistic is given by

*
ADup+ = sqrt(n) sup((j/n - zj)/(1 - zj))*

*
ADup- = sqrt(n) sup((zj - (j-1)/n)/(1 - zj))*

*ADup = max(ADup+, ADup-)*

with *zH=F_theta(H)* and *zj=F_theta(xj)*,
where *x_1, …, x_n* are the ordered data values. Here, *F_theta* is the
null distribution.

A list with class "mchtest" containing the following components

`statistic` |
the value of the Supremum Class Upper Tail Anderson-Darling statistic |

`treshold` |
the treshold value |

`p.value` |
the p-value of the test |

`data.name` |
a character string giving the name of the data |

`method` |
the character string "Supremum Class Upper Tail Anderson-Darling test" |

`alternative` |
the alternative |

`sim.no` |
number of simulated szenarios in the Monte-Carlo simulation |

Chernobay, A., Rachev, S., Fabozzi, F. (2005), *Composites goodness-of-fit tests
for left-truncated loss samples*, Tech. rep., University of Calivornia Santa Barbara

`ks.test`

, `v.test`

, `ad.test`

for supremum class tests and `ad2.test`

, `w2.test`

for other quadratic class tests. For more details see `mctest`

.

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