Applied Stochastic Models in Business and Industry最新文献

This paper focuses on the weighted mean residual life (WMRL) in mixtures of time to failure distributions. WMRL is an aging index that accounts for transformations of nonnegative random variables. The time to failure of systems operating under changing environments is described by mixtures of distributions that capture the corresponding random effects. This study analyzes the preservation by mixtures of aging properties based on the WMRL and bending properties. The latter compare the WMRL of the mixture and the expected value of the WMRL of the distributions therein. We also analyze the combined effect of a frailty and lifetime functions in the case of mixtures following the proportional WMRL model. The results reveal the improved behavior in the WMRL of mixtures with respect to that in the sub-populations in the mixture. This pattern is relevant for the maintenance of systems.

We propose here a new multivariate Birnbaum-Saunders (BS-type) distribution characterized by its leptokurtic property, making it particularly useful in the field of finance. Unlike the approach of Romeiro et al., our proposal is also based on scale mixtures of normal distributions (SMN), but with the mixing variable following a BS distribution, resulting in an asymmetric distribution. This new distribution captures leptokurtic character in the distribution, which implies heavier tails and a more pronounced peak compared to BS or StBS distributions (BS based on the Student-t distribution), enabling more realistic modeling of financial data. The resulting multivariate BS-type distribution is an absolutely continuous distribution whose marginal and conditional distributions have leptokurtic properties as compared to the usual univariate BS distribution. These results are a potentially necessary supplement to the recent work of Romeiro et al. This new distribution has not been discussed yet in the literature, and it enriches the family of multivariate BS distributions as it adds new features that take advantage of the presence of observations quite concentrated around the mode. By using the nice hierarchical representation, we have developed a fast and accurate EM (Expectation-Maximization) algorithm for computing the maximum likelihood estimates, and simulation studies show its good performance, and the corresponding asymptotic properties of the estimates. Finally, we illustrate the results with a real dataset, showcasing the effectiveness and practical utility of the proposed distribution.

In this article, an informative Bayesian approach is proposed for the bounded transformed gamma process, a novel stochastic process recently proposed in the literature to describe bounded above, monotonic increasing, degradation phenomena. The proposed approach is used to analyze a set of real wear data of the cylinder liners of a Diesel engine. Several scenarios, which differ in terms of the quality of the available prior knowledge, are considered and suitable prior distributions are suggested for each of them. In addition, detailed instructions are provided to help potential users incorporate into the suggested prior distributions all and solely the pieces of prior information that are available and sound. In particular, weak prior distributions are also suggested for situations in which available information is poor and/or there is no prior information to exploit. The proposed approach is used to estimate the process parameters and some functions thereof, such as the mean degradation level, the residual reliability of a unit, and to predict the future degradation growth and the useful lifetime. Point estimation and prediction under the (asymmetric) general entropy loss function are also performed to properly deal with situations where overestimation is costlier than underestimation, or vice versa. Estimates and predictions are computed by using proper Markov Chain Monte Carlo algorithms. Results obtained by analyzing wear data of the liners are compared both with those provided by classical methods and with those obtained by using Bayesian approaches based on vague priors. Finally, a sensitivity analysis is developed to study the impact of different prior distributions on the estimates of the parameters.

Measurement system analysis aims to quantify the variability in data attributable to the measurement system and evaluate its contribution to overall data variability. This paper conducts a rigorous theoretical investigation of the statistical methods used in such analyses, focusing on variance components and other critical parameters. While established techniques exist for single-variable cases, a systematic theoretical exploration of their properties has been largely overlooked. This study addresses this gap by examining estimators for variance components and other key parameters in measurement system assessment, analyzing their statistical properties, and providing new insights into their reliability, performance, and applicability.

Fairness is a key requirement for artificial intelligence applications. The assessment of fairness is typically based on group-based measures, such as statistical parity, which compares the machine learning output for the different population groups of a protected variable. Although intuitive and simple, statistical parity may be affected by the presence of control variables, correlated with the protected variable. To remove this effect, we propose to employ Shapley values, which measure the additional difference in output specifically due to the protected variable. To remove the possible impact of correlations on Shapley values, we compare them across different subgroups of the most correlated control variables, checking for the presence of Simpson's paradox, for which a fair model may become unfair when conditioning on a control variable. We also show how to mitigate unfairness by means of a propensity score matching that can improve statistical parity, building a training sample that matches similar individuals in different protected groups. We apply our proposal to a real-world database containing 157,269 personal lending decisions and show that both logistic regression and random forest models are fair when all loan applications are considered, but become unfair for high loan amounts requested. We show how propensity score matching can mitigate this bias.

The supermarket industry faces fierce competition in many geographic areas, with various brands competing for a market share that represents a significant portion of a country's GDP. For these businesses, understanding the factors that influence their sales and how they do so is crucial: location, pricing, quality, customer loyalty, and more. While much has been written about how these elements can affect revenue, there is a lack of existing models quantifying the monetary impact of having competitor stores within an own establishment area of influence. This article introduces a hierarchical Bayesian model that quantifies this impact for each product category within the brand's catalog. The model requires careful parameterization to adapt to the specific context, and therefore both its application and design represent a methodological novelty in this area. The main result is a matrix of coefficients that indicate the monetary effect of the presence of every competitor for each product category. The findings revealed by the model show that the influence of the proximity of each competitor does indeed vary depending on these categories. This information is valuable for the company when making decisions, such as choosing new store locations or determining the product assortment to offer in each establishment. The use of the results derived from this model provides a competitive advantage over others and helps to better understand the market by identifying which supermarket brands are the perceived leaders in each product category.