Multivariate Reversed Hazard Rates and Inactivity Times of Systems

The family of the multivariate conditional hazard rate functions often reveals to be a convenient tool to describe the joint probability distribution of a vector of non-negative random variables (lifetimes) in the absolutely continuous case. Such a tool can have in particular an important role in the study of the behavior of the minima among inter-dependent lifetimes. In this paper we introduce the concept of reversed multivariate conditional hazard rate functions, which extends the one-dimensional notion of reversed hazard rate of a single non-negative random variable. Several basic properties of this concept are proven. In particular, we point out a related role in the study of the behavior of the maximum value among inter-dependent lifetimes. In different applied fields, and in particular in the reliability literature, a remarkable class of dependence models for vectors of lifetimes is related with the load-sharing condition, which can be defined in terms of the multivariate conditional hazard rate functions. In the paper we define the class of reversed load-sharing models, which can be seen as natural extensions to the multivariate case of the univariate inverse exponential distributions. We analyze basic properties of such a class of dependence models. In particular we show a result related to the study of the inactivity time of a coherent system when the joint distribution of the components' lifetimes is a reversed load-sharing model

The Elasticity of a Random Variable as a Tool for Measuring and Assessing Risks

Elasticity is a very popular concept in economics and physics, recently exported and reinterpreted in the statistical field, where it has given form to the so-called elasticity function. This function has proved to be a very useful tool for quantifying and evaluating risks, with applications in disciplines as varied as public health and financial risk management. In this study, we consider the elasticity function in random terms, defining its probability distribution, which allows us to measure for each stochastic process the probability of finding elastic or inelastic situations (i.e., with elasticities greater or less than 1). This new tool, together with new results on the most notable points of the elasticity function covered in this research, offers a new approach to risk assessment, facilitating proactive risk management. The paper also includes other contributions of interest, such as new results that relate elasticity and inverse hazard functions, the derivation of the functional form of the cumulative distribution function of a probability model with constant elasticity and how the elasticities of functionally dependent variables are related. The interested reader can also find in the paper examples of how elasticity cumulative distribution functions are calculated, and an extensive list of probability models with their associated elasticity functions and distributions

Stochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included

Current Topics on Risk Analysis: ICRA6 and RISK2015 Conference

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Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio

Using model systems to investigate the effects of captivity on phenotypic variation: implications for captive breeding programmes

Captive breeding programmes (CBPs) offer a method for preventing the extinction of threatened species by assisting with species recovery, primarily by generating animals for reintroduction and supplementing wild populations. However, CBPs often have difficulty establishing self-sustaining populations, unable to maintain consistent reproduction and survivorship in captivity for reintroducing animals back into the wild. A contributing factor leading to this issue may be captive conditions producing phenotypes that differ from wild phenotypes. These phenotypic changes may lead to captive individuals having reduced survivorship, as well as reduced reproductive success, both in captivity and following reintroduction. Ultimately, a range of factors will determine the success of reintroductions; however, the phenotypic changes occurring in captivity, and how this may impact reintroduction success remains largely unknown. In this thesis, I outline how an animal’s phenotype may contribute to the success or failure of CBPs, and in turn, reintroduction success. I used a mammalian and an amphibian species as models to examine phenotypic changes in captivity and specifically looked at developmental, morphological and behavioural phenotypes