Description Usage Arguments Details Value References See Also Examples

Cram/'er-von Mises test providing a comparison of a fitted distribution with the empirical distribution.

1 |

`x` |
a numeric vector of data values |

`distn` |
character string naming the null distribution |

`fit` |
list of null distribution parameters |

`H` |
a treshold value |

`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 Cram/'er-von Mies test compares the null distribution with the empirical distribution function of the observed data, where left truncated data samples are allowed. The test statistic is given by

*
W2 = n/3 + n zH/(1-zH) + 1/(n (1-zH)) sum((1-2j) zj) + 1/(1-zH)^2 sum(zj-zH)^2*

with *z_H = F_theta(H)* and *
z_j=F_theta(x_j)*, 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 Cram\'er-von Mies 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 "Cramer-von Mises test" |

`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

`ad2up.test`

, `ad2.test`

for other quadratic class tests
and `ks.test`

, `v.test`

, `adup.test`

, `ad.test`

for supremum class tests. For more details see `mctest`

.

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