A stress–strength model with dependent variables to measure household financial fragility

The paper is inspired by the stress?Cstrength models in the reliability literature, in which given the strength (Y) and the stress (X) of a component, its reliability is measured by P(X < Y). In this literature, X and Y are typically modeled as independent. Since in many applications such an assumption might not be realistic, we propose a copula approach in order to take into account the dependence between X and Y. We then apply a copula-based approach to the measurement of household financial fragility. Specifically, we define as financially fragile those households whose yearly consumption (X) is higher than income (Y), so that P(X > Y) is the measure of interest and X and Y are clearly not independent. Modeling income and consumption as non-identically Dagum distributed variables and their dependence by a Frank copula, we show that the proposed method improves the estimation of household financial fragility. Using data from the 2008 wave of the Bank of Italy??s Survey on Household Income and Wealth we point out that neglecting the existing dependence in fact overestimates the actual household fragility.     

Maximum likelihood estimation in Dagum distribution with censored samples

In this work, we show that the Dagum distribution [3 Dagum, C. 1977. A new model of personal income distribution: Specification and estimation. Econ. Appl., XXX: 413–436.  [Google Scholar]] may be a competitive model for describing data which include censored observations in lifetime and reliability problems. Maximum likelihood estimates of the three parameters of the Dagum distribution are determined from samples with type I right and type II doubly censored data. We perform an empirical analysis using published censored data sets: in certain cases, the Dagum distribution fits the data better than other parametric distributions that are more commonly used in survival and reliability analysis. Graphical comparisons confirm that the Dagum model behaves better than a number of competitive distributions in describing the empirical hazard rate of the analyzed data. A probability plot to provide graphical check of the appropriateness of the Dagum model for right censored data is constructed, and the details are given in the appendix. Finally, a simulation study that shows the good performance of the maximum likelihood estimators of the Dagum shape parameters for finite type II doubly censored samples is carried out.     

A new generalized weighted Weibull distribution with decreasing,increasing, upside-down bathtub,N-shape and M-shape hazard rate

Recently, Domma et al. [An extension of Azzalinis method, J. Comput. Appl. Math. 278 (2015), pp. 37–47] proposed an extension of Azzalini's method. This method can attract readers due to its flexibility and ease of applicability. Most of the weighted Weibull models that have been introduced are with monotonic hazard rate function. This fact limits their applicability. So, our aim is to build a new weighted Weibull distribution with monotonic and non-monotonic hazard rate function. A new weighted Weibull distribution, so-called generalized weighted Weibull (GWW) distribution, is introduced by a method exposed in Domma et al. [13]. GWW distribution possesses decreasing, increasing, upside-down bathtub, N-shape and M-shape hazard rate. Also, it is very easy to derive statistical properties of the GWW distribution. Finally, we consider application of the GWW model on a real data set, providing simulation study too.     

Statistical Modeling of Temporal Dependence in Financial Data via a Copula Function

In financial analysis it is useful to study the dependence between two or more time series as well as the temporal dependence in a univariate time series. This article is concerned with the statistical modeling of the dependence structure in a univariate financial time series using the concept of copula. We treat the series of financial returns as a first order Markov process. The Archimedean two-parameter BB7 copula is adopted to describe the underlying dependence structure between two consecutive returns, while the log-Dagum distribution is employed to model the margins marked by skewness and kurtosis. A simulation study is carried out to evaluate the performance of the maximum likelihood estimates. Furthermore, we apply the model to the daily returns of four stocks and, finally, we illustrate how its fitting to data can be improved when the dependence between consecutive returns is described through a copula function.     

A copula-based approach to account for dependence in stress-strength models

The focus of stress-strength models is on the evaluation of the probability R = P(Y < X) that stress Y experienced by a component does not exceed strength X required to overcome it. In reliability studies, X and Y are typically modeled as independent. Nevertheless, in many applications such an assumption may be unrealistic. This is an interesting methodological issue, especially as the estimation of R for dependent stress and strength has received only limited attention to date. This paper aims to fill this gap by evaluating R taking into account the association between X and Y via a copula-based approach. We calculate a closed-form expression for R by modeling the dependence through a Farlie-Gumbel-Morgenstern copula and one of its extensions, numerical solutions for R are, instead, provided when members of Frank’s copula family are employed. The marginal distributions are assumed to belong to the Burr system (i.e. Burr III, Dagum or Singh-Maddala type). In all the cases, we prove that neglect of the existing dependence leads to higher or lower values of R than is the case.     

Asymptotic Distribution of the Maximum Likelihood Estimators of the Parameters of the Right-Truncated Dagum Distribution

In this work we have determined the asymptotic distribution of the maximum likelihood estimators of the parameters β, λ, and δ for the right-truncated Dagum model. Some numerical comparisons show that, for each combination of the parameters and for each sample size, the variance of maximum likelihood estimators increases as the truncation point decreases, i.e., with the increase in the cut of the right tail of distribution.     

The Beta-Dagum Distribution: Definition and Properties

This article introduces a five-parameter Beta-Dagum distribution from which moments, hazard and entropy, and reliability measures are then derived. These properties show the high flexibility of the said distribution. The maximum likelihood estimators of the Beta-Dagum parameters are examined and the expected Fisher information matrix provided. Next, a simulation study is carried out which shows the good performance of maximum likelihood estimators for finite samples. Finally, the usefulness of the new distribution is illustrated through real data sets.     

Some developments on the log-Dagum distribution

Skewed and fat-tailed distributions frequently occur in many applications. Models proposed to deal with skewness and kurtosis may be difficult to treat because the density function cannot usually be written in a closed form and the moments might not exist. The log-Dagum distribution is a flexible and simple model obtained by a logarithmic transformation of the Dagum random variable. In this paper, some characteristics of the model are illustrated and the estimation of the parameters is considered. An application is given with the purpose of modeling kurtosis and skewness that mark the financial return distribution.