A new least squares method for estimation and prediction based on the cumulative Hazard function

In this paper, the cumulative hazard function is used to solve estimation and prediction problems for generalized ordered statistics (defined in a general setup) based on any continuous distribution. The suggested method makes use of Rényi representation. The method can be used with type Ⅱ right-censored data as well as complete data. Extensive simulation experiments are implemented to assess the efficiency of the proposed procedures. Some comparisons with the maximum likelihood (ML) and ordinary weighted least squares (WLS) methods are performed. The comparisons are based on both the root mean squared error (RMSE) and Pitman's measure of closeness (PMC). Finally, two real data sets are considered to investigate the applicability of the presented methods

Reconstructing past fractional record values

In this paper, reconstructing past fractional upper (lower) records from any absolutely continuous distribution is proposed. For this purpose, two pivotal quantities are given and their exact distributions are derived. More detailed results, including the case of unknown parameters, are given for the exponential and Fre´chet distributions. Moreover, the exact mean square reconstructor errors are obtained and some comparisons between the pivotal quantities are performed. To explore the efficiency of the obtained results, a simulation study is conducted and two real data sets are analyzed

Asymptotic theory of extreme dual generalized order statistics

In a wide subclass of dual generalized order statistics (dgos) (which contains the most important models of descendingly ordered random variables), when the parameters [gamma]1,...,[gamma]n are assumed to be pairwise different, we study the weak convergence of the lower extremes, under general strongly monotone continuous transformations. It is revealed that the weak convergence of the maximum order statistics guarantees the weak convergence of any lower extreme dgos. Moreover, under linear and power normalization and by a suitable choice of these normalizations, the possible weak limits of any rth upper extreme order statistic are the same as the possible weak limits of the rth lower extreme dgos.

Asymptotic distribution of normalized maximum under finite mixture models

In this paper, we study the asymptotic distribution of the generally normalized maximum under finite mixture models. In one of the two theorems presented, we obtain a necessary and sufficient condition for this weak convergence, as well as the limit forms. The second theorem gives sufficient conditions for this convergence when the components of the mixture have different general normalizations. Examples are given to illustrate the applications of the two theorems.Mixture distributions Weak convergence l-max stable laws p-max stable laws General normalization Domains of attraction

Comparison between the rates of convergence of extremes under linear and under power normalization

Regular variation, ℓ-max-stable laws, p-max-stable laws, Uniform metric, Total variation matric, Primary 60F05, 62E20, Secondary 62E15, 62G30,