This paper proposes a novel Pearson-type quasi maximum likelihood estimator (QMLE) of GARCH($p, q$) models. Unlike the existing Gaussian QMLE, Laplacian QMLE, generalized non-Gaussian QMLE, or LAD estimator, our Pearsonian QMLE (PQMLE) captures not the heavy-tailed but also the skewed...

Maximum likelihood parameter estimation becomes easy by augmenting the parameter space of the probability distribution. A newly proposed extended model of the four-parameter generalized gamma distribution includes the three-parameter generalized extreme-value distribution which includes the...

The Weibull distribution was discovered by Rosin, Rammler, Sperling and Bennett between 1932 and 1936 in the context of particle measurement. Weibull found the same distribution a little later while investigating the strength of materials. More than 10 years after, in 1951, he finally showed...

For arbitrary stationary sequences of random variables satisfying a mild mixing condition, distributional approximations are established for functionals of clusters of exceedances over a high threshold.The approximations are in terms of the distribution of the process conditionally on the event...