Description Usage Arguments Details Value Author(s) References Examples

This function compute mean of order p (MOP) basic statistic for the extreme value index (EVI), which is indeed a simple generalisation of the Hill estimator.

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`x` |
Data vector. |

`k` |
a vector of number of upper order statistics. |

`p` |
a vector of mean order. |

`method` |
Method used, ("MOP", default) and reduced-bias MOP ("RBMOP"). |

Basic statistics for the EVI estimation, the MOP of *U_{ik}*, where
*U_{ik}= \frac{X_{n-i+1:n}}{X_{n-k:n}} * and *X_{i:n}* are order statistics, is

*A(k)= ( \frac{1}{k} ∑^k_{i=1} U^p_{ik} )^{1/p},*

for *p \neq 0.*

The new class of MOP EVI- estimators is

*H_p(k)= (1 - A^{-p}(k))/p,*

for *p \neq 0.*
At `p=0`

the above MOP estimator is equal to classical Hill estimator.

Reduced bias MOP EVI-estimators is

*RBA(k)=H_p(k) (1- \frac{β (1-p H_p(k) )}{1-ρ-p H_p(k)} (\frac{n}{k})^ρ ).*

a matrix of EVI estimates, corresponds to `k`

row and `p`

columns. When `Method = "RBMOP"`

shape and scale second order parameters estimates are also returned.

B G Manjunath [email protected], Frederico Caeiro [email protected]

Brilhante, M.F., Gomes, M.I. and Pestana, D. (2013). A simple generalisation of the Hill estimator.
*Computational Statistics and Data Analysis*, **57**, 518– 535.

Beran, J., Schell, D. and Stehlik, M. (2013). The harmonic moment tail index estimator: asymptotic distribution and robustness. *Ann Inst Stat Math*, Published Online.

Gomes, M.I., Brilhante, M.F. and Pestana, D. (2013). New reduced-bias estimators of a positive extreme value index. *Submitted article*.

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evt0 documentation built on May 30, 2017, 6:10 a.m.

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