Preservation of stochastic orders through the system signature has captured the attention of researchers in recent years. Signature-based comparisons have been made for the usual stochastic order, hazard rate order, and likelihood ratio orders. However, for the mean residual life (MRL) order, it has recently been proved that the preservation result does not hold true in general, but rather holds for a particular class of distributions. In this paper, we study whether or not a similar preservation result holds for the mean inactivity time (MIT) order. We prove that the MIT order is not preserved from signatures to system lifetimes with independent and identically distributed (i.i.d.) components, but holds for special classes of distributions. The relationship between these classes and the order statistics is also highlighted. Furthermore, the distribution-free comparison of the performance of coherent systems with dependent and identically distributed (d.i.d.) components is studied under the MIT ordering, using diagonal-dependent copulas and distorted distributions.

Recently, the relevation transformation has received further attention from researchers, and some interesting results have been developed. It is well known that the active redundancy at component level results in a more reliable coherent system than that at system level. However, the lack of study of this problem with relevation redundancy prevents us from fully understanding such a generalization of the active redundancy. In this note we deal with relevation redundancy to coherent systems of homogeneous components. Typically, for a series system of independent components, we have proved that the lifetime of a system with relevation redundancy at component level is larger than that with relevation redundancy at system level in the sense of the usual stochastic order and the likelihood ratio order, respectively. For a coherent system with dependent components, we have developed a sufficient condition in terms of the domination function to the usual stochastic order between the system lifetime with redundancy at component level and that at system level.

This article investigates the development of wh-in-situ questions in French by examining a three-year kindergarten dataset of spontaneous productions with 16 children between 2;5 and 5;11. The distribution of the wh-phrases is statistically examined in relation to age, verb form (Fixed be form c’est ‘it is’ vs. Free be forms vs. Free lexical verbs), and grammatical category of the wh-word (Pronoun vs. Adverb). Results show that wh-in-situ remains prevalent throughout the period despite a steady increase in wh-ex-situ. Verb form (Fixed vs. All free forms) is a discriminating variable for the wh-position in all three years, and it interacts with the category of the wh-word. The Fixed be form c’est favours in-situ wh-pronouns (c’est qui Taz ?), whereas the Free forms favour wh-ex-situ questions, and massively co-occur with wh-adverbs (combien ça coûte ?). The emergence of the ex-situ qu’est-ce que ‘what is it that’, as opposed to the in-situ quoi ‘what’, is identified as a factor accounting for the gradual increase in wh-ex-situ. Finally, most outliers (wh-in-situ with Free forms) are shown to belong to the same paradigm as c’est in-situ questions: non-presuppositional questions, which are visible from the frequent use of là ‘there’, like c’est, a deictic item.

Quantifying tail dependence is an important issue in insurance and risk management. The prevalent tail dependence coefficient (TDC), however, is known to underestimate the degree of tail dependence and it does not capture non-exchangeable tail dependence since it evaluates the limiting tail probability only along the main diagonal. To overcome these issues, two novel tail dependence measures called the maximal tail concordance measure (MTCM) and the average tail concordance measure (ATCM) are proposed. Both measures are constructed based on tail copulas and possess clear probabilistic interpretations in that the MTCM evaluates the largest limiting probability among all comparable rectangles in the tail, and the ATCM is a normalized average of these limiting probabilities. In contrast to the TDC, the proposed measures can capture non-exchangeable tail dependence. Analytical forms of the proposed measures are also derived for various copulas. A real data analysis reveals striking tail dependence and tail non-exchangeability of the return series of stock indices, particularly in periods of financial distress.

In this paper, we study the estimation of a scale parameter from a sample of lifetimes of coherent systems with a fixed structure. We assume that the components are independent and identically distributed having a common distribution which belongs to a scale parameter family. Some results are obtained as well for dependent (exchangeable) components. To this end, we will use the representations for the distribution function of a coherent system based on signatures. We prove that the efficiency of the estimators depends on the structure of the system and on the scale parameter family. In the dependence case, it also depends on the baseline copula function.

The distribution of human leukocyte antigens in the population assists in matching solid organ donors and recipients when the typing methods used do not provide sufficiently precise information. This is made possible by linkage disequilibrium (LD), where alleles co-occur more often than random chance would suggest. There is a trade-off between the high bias and low variance of a broad sample from the population and the low bias but high variance of a focused sample. Some of this trade-off could be alleviated if sub-populations shared LD despite having different allele frequencies. These experiments show that Bayesian estimation can balance bias and variance by tuning the effective sample size of the reference panel, but the LD as represented by an additive or multiplicative copula is not shared.

The choice of a copula model from limited data is a hard but important task. Motivated by the visual patterns that different copula models produce in smoothed density heatmaps, we consider copula model selection as an image recognition problem. We extract image features from heatmaps using the pre-trained AlexNet and present workflows for model selection that combine image features with statistical information. We employ dimension reduction via Principal Component and Linear Discriminant Analyses and use a Support Vector Machine classifier. Simulation studies show that the use of image data improves the accuracy of the copula model selection task, particularly in scenarios where sample sizes and correlations are low. This finding indicates that transfer learning can support statistical procedures of model selection. We demonstrate application of the proposed approach to the joint modelling of weekly returns of the MSCI and RISX indices.

The study provides comparative risk analyses of Australia’s three Victorian dairy regions. Historical data were used to identify business risk and financial viability. Multivariate distributions were fitted to the historical price, production, and input costs using copula models, capturing non-linear dependence among the variables. Monte Carlo simulation methods were then used to generate cash flows for a decade. Factors that influenced profitability the most were identified using sensitivity analysis. The dairies in the Northern region have faced water reductions, whereas those of Gippsland and South West have more positive indicators. Our analysis summarizes long-term risks and net farm profits by utilizing survey data in a probabilistic manner.

This paper investigates the issue of stochastic comparison of multi-active redundancies at the component level versus the system level. Based on the assumption that all components are statistically dependent, in the case of complete matching and nonmatching spares, we present some interesting comparison results in the sense of the hazard rate, reversed hazard rate and likelihood ratio orders, respectively. And we also obtain two comparison results between relative agings of resulting systems at the component level and the system level. Several numerical examples are provided to illustrate the theoretical results.

A widely accepted assumption in both the syntactic and semantic literature is that copulas lack semantic content. A consequent question is how to explain the existence in certain languages of two copular verbs that give rise to different interpretations. Such is the case in numerous languages of the Dene family (formerly known as Athapaskan). We explain this situation with the hypothesis that the copulas realize an underlying three-copula system differing in argument structure. Differences between the interpretations of copular clauses in these languages originate in the compositional semantics of these structures, not in any lexical semantic differences.

This hypothesis successfully predicts the distributional differences between the surface forms of the Dene copulas, such as their compatibility with adjuncts of time and intentionality, interactions with accusative case, and semantic lifetime effects.

This paper examines correlation and dependence structures between money and the level of economic activity in the USA in the context of a Markov-switching copula vector error correction model. We use the error correction model to focus on the short-run dynamics between money and output while accounting for their long-run equilibrium relationship. We use the Markov regime-switching model to account for instabilities in the relationship between money and output, and also consider different copula models with different dependence structures to investigate (upper and lower) tail dependence.

The mvClaim package in R provides flexible modelling frameworks for multivariate insurance claim severity modelling. The current version of the package implements a parsimonious mixture of experts (MoE) model family with bivariate gamma distributions, as introduced in Hu et al., and a finite mixture of copula regressions within the MoE framework as in Hu & O’Hagan. This paper presents the modelling approach theory briefly and the usage of the models in the package in detail. This package is hosted on GitHub at https://github.com/senhu/.

Previous comprehension studies using Picture Matching Tasks (PMT) have shown that, by the age of four, Spanish-speaking children have acquired the semantics of estar being able to calculate the implicature that a property introduced with estar does not hold independent of time as well as displaying some ability to integrate discourse information about properties that change in the course of a story. This study extends that line of research to children under the age of four. Thirty-eight monolingual Spanish-speaking children were tested in two PMTs. The results show that at age three children differ from older children in their interpretation of the copulas suggesting that the distinction between ser and estar with adjectives emerges between the ages of three and four.