The mean residual life (MRL) function is an important function in survival analysis, actuarial science, economics and other social sciences and reliability for characterizing lifetime. Different methods have been proposed for doing inference on the MRL but their coverage probabilities for small...

Graphing univariate distributions is central to both statistical graphics, in general, and StataÕs graphics, in particular. Now that Stata 8 is out, a review of official and user-written commands is timely. The emphasis here is on going beyond what is obviously and readily available, with...

Using daily observations of the index and stock market returns for the Peruvian case from January 3, 1990 to May 31, 2013, this paper models the distribution of daily loss probability, estimates maximum quantiles and tail probabilities of this distribution, and models the extremes through a...

Extreme value theory for a class of EGARCH processes is developed. It is shown that the EGARCH process as well as the logarithm of its conditional variance lie in the domain of attraction of the Gumbel distribution. Norming constants are obtained and it is shown that the considered processes...

The multinomial logit model in discrete choice analysis is widely used in transport research. It has long been known that the Gumbel distribution forms the basis of the multinomial logit model. Although the Gumbel distribution is a good approximation in some applications such as route choice...

Emil J. Gumbel ist der Namensgeber der jährlichen Gumbel-Vorlesung auf der Statistischen Woche. Leider ist der Namensgeber dieser Vorlesung nur noch wenigen Teilnehmern und Vortragenden bekannt. Dieser Artikel möchten diesem Defizit abhelfen. Denn Gumbel war nicht nur der Namensgeber...

Using daily observations of the index and stock market returns for the Peruvian case from January 3, 1990 to May 31, 2013, this paper models the distribution of daily loss probability, estimates maximum quantiles and tail probabilities of this distribution, and models the extremes through a...

The logsum formula, which provides the expected maximum utility for the multinomial logit model, is often used as a measure of welfare. We provide here a closed form formula of the welfare measure of an individual who has not access to his first-best choice, but has access to his rth-best...

We show that the number of individuals selecting their worst alternatives within a finite set of alternatives can be written as an alternating sum of the number of individuals having their best choice within subset of alternatives. The identities are then applied to random utility models,...

Extreme value theory is the most scientific approach to an inherently difficult problem - predicting the possibility that an extreme event will occur. Broadly speaking, there are two kinds of models for extreme values. The first group of models are models for a distribution of normalized maximum...