On a class exhibiting trend change in average failure rate

Abstract

Weak convergence and moment convergence issues are investigated for the New Better than Average Failure Rate (NBAFR) family (introduced by Loh (1984 Loh, W. Y. 1984. A new generalization of the class of NBU distributions. IEEE Transactions on Reliability R-33 :97–113[Crossref], [Web of Science ®] , [Google Scholar])). We explore the validity of these results in the context of a more general ageing class that we introduce. We prove some new properties of this class and derive its interrelationships with other non-monotonic ageing families. Reliability and moment bounds are obtained and an interesting characterization of exponentiality is proved. Special cases of our results lead to new theorems for the NBAFR class. Finally weak convergence and related issues are established for this class.     

Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution

Summary . A fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is sufficiently general to encompass some recent proposals in the literature, variously related to the skew normal distribution. The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work. The final part of the paper specializes further to a form of multivariate skew t -density. Likelihood inference for this distribution is examined, and it is illustrated with numerical examples.     

Estimation of noncentrality parameters

We propose some estimators of noncentrality parameters which improve upon usual unbiased estimators under quadratic loss. The distributions we consider are the noncentral chi-square and the noncentral F. However, we give more general results for the family of elliptically contoured distributions and propose a robust dominating estimator.     

Bayesian analysis of a marked point process: Application in seismic hazard assessment

Point processes are the stochastic models most suitable for describing physical phenomena that appear at irregularly spaced times, such as the earthquakes. These processes are uniquely characterized by their conditional intensity, that is, by the probability that an event will occur in the infinitesimal interval (t, t+Δt), given the history of the process up tot. The seismic phenomenon displays different behaviours on different time and size scales; in particular, the occurrence of destructive shocks over some centuries in a seismogenic region may be explained by the elastic rebound theory. This theory has inspired the so-called stress release models: their conditional intensity translates the idea that an earthquake produces a sudden decrease in the amount of strain accumulated gradually over time along a fault, and the subsequent event occurs when the stress exceeds the strength of the medium. This study has a double objective: the formulation of these models in the Bayesian framework, and the assignment to each event of a mark, that is its magnitude, modelled through a distribution that depends at timet on the stress level accumulated up to that instant. The resulting parameter space is constrained and dependent on the data, complicating Bayesian computation and analysis. We have resorted to Monte Carlo methods to solve these problems.     

Weak disintegrability as a form of preservation of coherence

Summary Weak disintegrations are investigated from various points of view. Kolmogorov's definition of conditional probability is critically analysed, and it is noted how the notion of disintegrability plays some role in connecting Kolmogorov's definition with the one given in line with de Finetti's coherence principle. Conditions are given, on the domain of a prevision, implying the equivalence between weak disintegrability and conglomerability. Moreover, weak sintegrations are characterized in terms of coherence, in de Finetti's sense, of, a suitable function. This fact enables us to give, an interpretation of weak disintegrability as a form of “preservation of coherence”. The previous results are also applied to a hypothetical inferential problem. In particular, an inference is shown to be coherent, in the sense of Heath and Sudderth, if and only if a suitable function is coherent, in de Finetti's sense. Research partially supported by: M.U.R.S.T. 40% “Problemi di inferenza pura”.     

Contre-exemple au théorème de P.C. Consul sur la factorisation des distributions de Poisson généralisées

This note exhibits two independent random variables on integers, X₁ and X₂, such that neither X₁ nor X₂ has a generalized Poisson distribution, but X₁ + X₂ has. This contradicts statements made by Professor Consul in his recent book.     

SHOULD WE ESTIMATE THE PROBABILITY OF CORRECT SELECTION?

Various authors, given k location parameters, have considered lower confidence bounds on (standardized) dserences between the largest and each of the other k - 1 parameters. They have then used these bounds to put lower confidence bounds on the probability of correct selection (PCS) in the same experiment (as was used for finding the lower bounds on differences). It is pointed out that this is an inappropriate inference procedure. Moreover, if the PCS refers to some later experiment it is shown that if a non-trivial confidence bound is possible then it is already possible to conclude, with greater confidence, that correct selection has occurred in the first experiment. The short answer to the question in the title is therefore ‘No’, but this should be qualified in the case of a Bayesian analysis.     

近代河南集市研究再思考

近代集市的发展不仅表现为数量方面的增加,也有集市数量不变而集市承载量增加的情况;考察集市分布密度以耕地面积为基础更有可比性,而且开市率的高低主要是人们传统习惯、人口规模、集市密度、商品化程度、经济发展状况等因素综合作用的结果,其中传统习惯对开市率的影响较大。     

BATHTUB-TYPE CURVES IN RELIABILITY AND BEYOND

Finding optimal, or at least good, maintenance and repair policies is crucial in reliability engineering. Likewise, describing life phases of human mortality is important when determining social policy or insurance premiums. In these tasks, one searches for distributions to fit data and then makes inferences about the population(s). In the present paper, we focus on bathtub‐type distributions and provide a view of certain problems, methods and solutions, and a few challenges, that can be encountered in reliability engineering, survival analysis, demography and actuarial science.