Description Usage Arguments Details Value References See Also Examples

Quadratic Class Upper Tail Anderson-Darling test providing a comparison of a fitted distribution with the empirical distribution.

1 | ```
ad2up.test(x, distn, fit, H = NA, sim = 100, tol = 1e-04, estfun = NA)
``` |

`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 Anderson-Darling 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

*
AD2up = -2n log(1-zH) + 2 sum(log(1-zj)) + (1-zH)/n sum((1 + 2(n-j))/(1-zj))*

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 Quadratic 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 "Quadratic Class Upper Tail Anderson-Darling 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

`ad2.test`

, `w2.test`

for other quadratic class tests
and `ks.test`

, `v.test`

, `adup.test`

, `ad.test`

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

.

1 2 3 4 5 | ```
set.seed(123)
treshold <- 10
xc <- rlnorm(100, 2, 2) # complete sample
xt <- xc[xc >= treshold] # left truncated sample
ad2up.test(xt, "plnorm", list(meanlog = 2, sdlog = 2), H = 10)
``` |

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