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The purpose of this paper is to investigate the stochastic comparisons of the parallel system with independent heterogeneous Gumbel components and series and parallel systems with independent heterogeneous truncated Gumbel components in terms of various stochastic orderings.

The obtained results in this paper are obtained by using the vector majorization methods and results. First, the components of series and parallel systems are heterogeneous and having Gumbel or truncated Gumbel distributions. Second, multiple-outlier truncated Gumbel models are discussed for these systems. Then, the relationship between the systems having Gumbel components and Weibull components are considered. Finally, Monte Carlo simulations are performed to illustrate some obtained results.

The reversed hazard rate and likelihood ratio orderings are obtained for the parallel system of Gumbel components. Using these results, similar new results are derived for the series system of Weibull components. Stochastic comparisons for the series and parallel systems having truncated Gumbel components are established in terms of hazard rate, likelihood ratio and reversed hazard rate orderings. Some new results are also derived for the series and parallel systems of upper-truncated Weibull components.

To the best of our knowledge thus far, stochastic comparisons of series and parallel systems with Gumbel or truncated Gumble components have not been considered in the literature. Moreover, new results for Weibull and upper-truncated Weibull components are presented based on Gumbel case results.

Fat‐tailed distributions have been found in many financial and economic variables ranging from forecasting returns on financial assets to modeling recovery distributions in bankruptcies. They have also been found in numerous insurance applications such as catastrophic insurance claims and in value‐at‐risk measures employed by risk managers. Financial applications include:

The potential advantage of extreme value theory in modeling management phenomena is the central theme of this paper. The statistics of extremes have played only a very limited role in management studies despite the disproportionate emphasis on unusual events in the world of managers. An overview of this theory and related statistical models is presented, and illustrative empirical examples provided.

This study aims to explore virtual site visit adoption patterns of US convention facilities based on the diffusion of innovation (DOI) theory. Additionally, it offers predictive models of virtual site visit tool adoption by applying probability distributions.

The study used content analysis of 369 US convention facility websites. Data collected from the websites recorded the presence or absence of the following tools facilitating virtual site visits: photos, floor plans, videos, 360-photos, 360-tours and virtual reality (VR)-optimized tours. The website content analysis was followed by application of the DOI theory and predictive modeling.

According to the DOI theory, the use of VR-optimized tours (4.34%) is still in the early adoption stage, followed by 360-degree tours (12.74%) and standard videos (17.89%) that have transitioned into the early majority stage of adoption and photos (72.09%) and floor plans (84.82%) that represent a late majority stage. Three predictive models with shifted Gompertz, Gumbel and Bass distributions forecasted that convention centers would achieve a 50% adoption rate of 360-degree tools (photos and tours) in 4.67, 4.2 and three years, respectively. The same models predicted a 50% adoption rate of 360-degree tours in 6.62, 5.81 and 4.42 years.

The research indicates that most US convention facilities have not taken full advantage of their websites as a sales and marketing tool.

This study is the first comprehensive attempt to evaluate the adoption rate of VR and other technologies enabling virtual site visits by using content analysis of US convention facility websites. Additionally, it is the first attempt to apply probability distributions to predict technology adoption in the convention industry context.

Purpose – In this chapter, copula theory is used to model dependence structure between hedge fund returns series.

Methodology/approach – Goodness-of-fit tests, based on the Kendall's functions, are applied as selection criteria of the “best” copula. After estimating the parametric copula that best fits the used data, we apply previous results to construct the cumulative distribution functions of the equally weighted portfolios.

Findings – The empirical validation shows that copula clearly allows better estimation of portfolio returns including hedge funds. The three studied portfolios reject the assumption of multivariate normality of returns. The chosen structure is often of Student type when only indices are considered. In the case of portfolios composed by only hedge funds, the dependence structure is of Franck type.

Originality/value of the chapter – Introducing goodness-of-fit bootstrap method to validate the choice of the best structure of dependence is relevant for hedge fund portfolios. Copulas would be introduced to provide better estimations of performance measures.

Copula modeling enables the analysis of multivariate count data that has previously required imposition of potentially undesirable correlation restrictions or has limited attention to models with only a few outcomes. This article presents a method for analyzing correlated counts that is appealing because it retains well-known marginal distributions for each response while simultaneously allowing for flexible correlations among the outcomes. The proposed framework extends the applicability of the method to settings with high-dimensional outcomes and provides an efficient simulation method to generate the correlation matrix in a single step. Another open problem that is tackled is that of model comparison. In particular, the article presents techniques for estimating marginal likelihoods and Bayes factors in copula models. The methodology is implemented in a study of the joint behavior of four categories of US technology patents. The results reveal that patent counts exhibit high levels of correlation among categories and that joint modeling is crucial for eliciting the interactions among these variables.

The polynomial dimensional decomposition (PDD) method is a popular tool to establish a surrogate model in several scientific areas and engineering disciplines. The selection of appropriate truncated polynomials is the main topic in the PDD. In this paper, an easy-to-implement adaptive PDD method with a better balance between precision and efficiency is proposed.

First, the original random variables are transformed into corresponding independent reference variables according to the statistical information of variables. Second, the performance function is decomposed as a summation of component functions that can be approximated through a series of orthogonal polynomials. Third, the truncated maximum order of the orthogonal polynomial functions is determined through the nonlinear judgment method. The corresponding expansion coefficients are calculated through the point estimation method. Subsequently, the performance function is reconstructed through appropriate orthogonal polynomials and known expansion coefficients.

Several examples are investigated to illustrate the accuracy and efficiency of the proposed method compared with the other methods in reliability analysis.

The number of unknown coefficients is significantly reduced, and the computational burden for reliability analysis is eased accordingly. The coefficient evaluation for the multivariate component function is decoupled with the order judgment of the variable. The proposed method achieves a good trade-off of efficiency and accuracy for reliability analysis.

The purpose of this paper is to analyse the effect of market risk on the revenues perceived by an agricultural producer, namely, a coffee exporter firm.

To model this risk, copula models and extreme value theory are used to perform more robust estimations, which take into account the multivariate dependence between the risk factors. As a final point, different quantitative measures of risk, such as the value at risk and the expected shortfall, are estimated as an indicator of the maximum expected loss.

One of the principal findings is that for an agricultural exporter firm, there is an optimal decision between exporting to another country and selling the commodity in the national market. The choice regarding the levels exported will determine the firm’s amount of risk and expected return.

One of the limitations found in modelling the risk/return of the firm is the data. Not much data on the structure of the firm can be found, and many of the firms are averse to providing such information.

The purpose of the paper is to create a measure of risk to analyse the future of the firm, generating a measure of expected risk and return that takes into account the uncertainty of the future. The applications can be applied to measure the risk of a potential investment and real option valuation.

This paper applied multiple coherent measures of financial risk to an agricultural commodity exporter firm. This can be novel, especially in the context of a non-financial firm.

La finalidad de este artículo es realizar un análisis del efecto del riesgo de mercado en el ingreso de un productor agrícola, específicamente, una firma exportadora de café.

Para modelar el riesgo, se hace uso de modelos a partir de Teoría del Valor Extremo y Cópulas, esto permite obtener estimaciones robustas en presencia de dependencia entre el conjunto de factores de riesgo. Finalmente, se estiman diferentes medidas cuantitativas de riesgo, como el Valor en Riesgo (VeR) y la Perdida Esperada (ES), como medidas de la máxima perdida esperada.

Uno de los principales resultados, es que para una firma exportadora agrícola, existe una decisión óptima entre exportar o vender el bien en el Mercado nacional. La elección de la cantidad exportada determinará la cantidad de riesgo y retorno a la que estará expuesta la firma.

La principal limitación en modelar el riesgo/retorno de la firma son los datos. No hay mayor información pública de la estructura de la firma, y en la mayoría de casos las firmas son adversas a proveer esta información para la investigación.

La finalidad del artículo es crear una medida de riesgo para analizar el futuro de la firma, esta aproximación al riesgo y retorno esperado tiene en cuenta la incertidumbre que afronta la firma del futuro. Las aplicaciones potenciales pueden ser el análisis de riesgo de una inversión y la valoración de una opción real.

Este artículo aplica diferentes medidas coherentes de riesgo financiero a una firma exportadora de bienes agrícolas. Esta metodología es innovadora, en especial en el contexto de firmas no financieras.

Many consumer choice situations are characterized by the simultaneous demand for multiple alternatives that are imperfect substitutes for one another. A simple and parsimonious multiple discrete-continuous extreme value (MDCEV) econometric approach to handle such multiple discreteness was formulated by Bhat (2005) within the broader Kuhn–Tucker (KT) multiple discrete-continuous economic consumer demand model of Wales and Woodland (1983). In this chapter, the focus is on presenting the basic MDCEV model structure, discussing its estimation and use in prediction, formulating extensions of the basic MDCEV structure, and presenting applications of the model. The paper examines several issues associated with the MDCEV model and other extant KT multiple discrete-continuous models. Specifically, the paper discusses the utility function form that enables clarity in the role of each parameter in the utility specification, presents identification considerations associated with both the utility functional form as well as the stochastic nature of the utility specification, extends the MDCEV model to the case of price variation across goods and to general error covariance structures, discusses the relationship between earlier KT-based multiple discrete-continuous models, and illustrates the many technical nuances and identification considerations of the multiple discrete-continuous model structure. Finally, we discuss the many applications of MDCEV model and its extensions in various fields.

The traditional predictor of technical inefficiency proposed by Jondrow, Lovell, Materov, and Schmidt (1982) is a conditional expectation. This chapter explores whether, and by how much, the predictor can be improved by using auxiliary information in the conditioning set. It considers two types of stochastic frontier models. The first type is a panel data model where composed errors from past and future time periods contain information about contemporaneous technical inefficiency. The second type is when the stochastic frontier model is augmented by input ratio equations in which allocative inefficiency is correlated with technical inefficiency. Compared to the standard kernel-smoothing estimator, a newer estimator based on a local linear random forest helps mitigate the curse of dimensionality when the conditioning set is large. Besides numerous simulations, there is an illustrative empirical example.