Copula-Based Bayesian Reliability Analysis of a Product of a Probability and a Frequency Model for Parallel Systems When Components Are Dependent

While the dependence assumption among the components is naturally important in evaluating the reliability of a system, studies investigating the issues of aggregation errors in Bayesian reliability analyses have been focused mainly on systems with independent components. This study developed a copula-based Bayesian reliability model to formulate dependency between components of a parallel system and to estimate the failure rate of the system. In particular, we integrated Monte Carlo simulation and classification tree learning to identify key factors that affect the magnitude of errors in the estimation of posterior means of system reliability (for different Bayesian analysis approaches—aggregate analysis, disaggregate analysis, and simplified disaggregate analysis) to provide important guidelines for choosing the most appropriate approach for analyzing a model of products of a probability and a frequency for parallel systems with dependent components.

Modeling risk dependence and portfolio VaR forecast through vine copula for cryptocurrencies

Risk in finance may come from (negative) asset returns whilst payment loss is a typical risk in insurance. It is often that we encounter several risks, in practice, instead of single risk. In this paper, we construct a dependence modeling for financial risks and form a portfolio risk of cryptocurrencies. The marginal risk model is assumed to follow a heteroscedastic process of GARCH(1,1) model. The dependence structure is presented through vine copula. We carry out numerical analysis of cryptocurrencies returns and compute Value-at-Risk (VaR) forecast along with its accuracy assessed through different backtesting methods. It is found that the VaR forecast of returns, by considering vine copula-based dependence among different returns, has higher forecast accuracy than that of returns under prefect dependence assumption as benchmark. In addition, through vine copula, the aggregate VaR forecast has not only lower value but also higher accuracy than the simple sum of individual VaR forecasts. This shows that vine copula-based forecasting procedure not only performs better but also provides a well-diversified portfolio.

Inter-specific Variability in Demographic Processes Affects Abundance-Occupancy Relationships

Species with large local abundances tend to occupy more sites. One of the mechanisms proposed to explain this widely reported inter-specific relationship is a cross-scale hypothesis based on dynamics at the population level. Called the vital rates mechanism, it uses within-population demographic processes of population growth and density dependence to explain how positive inter-specific abundance-occupancy relationships can arise. Even though the vital rates mechanism is mathematically simple, it has never been tested directly because of the difficulty in estimating the demographic parameters involved. Here, using a recently introduced mark-recapture analysis method on 17 bird species, we show that inter-specific variability in density dependence strength can weaken both abundance-occupancy relationships and the expected corollaries of the vital rates mechanism. We demonstrate that one of the key assumptions of vital rates mechanism, that density dependence strength should be similar among species, is not met for these 17 species. Additionally, the mathematical structure of vital rates mechanism that relate population-level abundance and intrinsic growth rate is only weakly observed in our data. We argue that this mismatch of mathematical structure and data together with the violation of density dependence assumption weakens the expected positive abundance-occupancy association. Vital rates mechanism also predicts conditions under which positive abundance-occupancy association is weakened or even reversed; our results are consistent with these predictions. More generally, our findings support a cross-scale mechanism of macroecological abundance-occupancy relationship emerging from density-dependent dynamics at the population level.

On the use of Archimedean copulas for insurance modelling

In this paper, we explore the use of an extensive list of Archimedean copulas in general and life insurance modelling. We consider not only the usual choices like the Clayton, Gumbel–Hougaard, and Frank copulas but also several others which have not drawn much attention in previous applications. First, we apply different copula functions to two general insurance data sets, co-modelling losses and allocated loss adjustment expenses, and also losses to building and contents. Second, we adopt these copulas for modelling the mortality trends of two neighbouring countries and calculate the market price of a mortality bond. Our results clearly show that the diversity of Archimedean copula structures gives much flexibility for modelling different kinds of data sets and that the copula and tail dependence assumption can have a significant impact on pricing and valuation. Moreover, we conduct a large simulation exercise to investigate further the caveats in copula selection. Finally, we examine a number of other estimation methods which have not been tested in previous insurance applications.

Weak law of large numbers for randomly indexed sequences of m-dependent random variables

First, we establish the inequalities related to the upper bound for the probability of the sum of a random number of random variables satisfying certain conditions. More specifically, in Theorem 1, these variables are assumed that get values on a bounded interval and in particular, are setting under m-dependence assumption instead of the usual independence, where independence is merely the specific case of m-dependence when m equal to 0. For a random index with a familiar distribution, it is possible to proceed to make reasonable estimates for the expected terms on the right-hand side of the two inequalities in Theorem 1 to obtain Chernoff-Hoeffding-style bounds. Those bounds will be employed to prove that there is a weak law of large numbers for the sequence of m-dependent random variables correspondingly and the convergence rate is exponential. Next, in Theorem 2, we had chosen the Poisson distributed index as a typical for presentation. Finally, this theorem is illustrated through an image which is constructed by simulated values of 1-dependent variables. Here, the way that we have applied to create a 1-dependent sequence from an independent sequence that it is likely will help readers understand more about m-dependence structure.

A generalized DEA model for inputs (outputs) estimation under inter-temporal dependence

This paper extended the inverse Data Envelopment Analysis (DEA) to the framework of dynamic DEA. The following question is studied under inter-temporal dependence assumption: among a set of decision making units (DMUs), to what extent should the input (output) levels of the DMU change if the efficiency index of a DMU remains unchanged, yet the output (input) levels change? This question is answered using (periodic weak) Pareto solutions of multiple-objective linear programming (MOLP) problems in the framework of dynamic DEA. In this study, unlike other proposed methods, the simultaneous increase and decrease of the various input (output) levels are considered under inter-temporal dependence. In addition, a numerical example with real data is provided to illustrate the objective of this research.

Extreme Conditional Tail Moment Estimation under Serial Dependence

A wide range of risk measures can be written as functions of conditional tail moments (CTMs) and value-at-risk (VaR), for instance the expected shortfall (ES). In this paper, we derive joint central limit theory for semi-parametric estimates of CTMs, including in particular ES, at arbitrarily small risk levels. We also derive confidence corridors for VaR at different levels far out in the tail, which allows for simultaneous inference. We work under a semi-parametric Pareto-type assumption on the distributional tail of the observations and only require an extremal-near epoch dependence assumption on the serial dependence. In simulations, our semi-parametric ES estimate is often shown to be more accurate in terms of mean absolute deviation than extant non- and semi-parametric estimates. An empirical application to the extreme swings in Volkswagen log-returns during the failed takeover attempt by Porsche illustrates the proposed methods.