NEW DEVELOPMENTS ON THE USE OF BIVARIATE RODRIGUEZ-BURR III DISTRIBUTION IN RELIABILITY STUDIES

In this paper we study the bivariate Rodriguez-Burr III distribution from a reliability point of view. In particular, we derive various functions used in reliability theory of conditional distributions, viz hazard rate, reversed hazard rate, mean residual life and mean reversed residual life and, using some notions of dependence, their monotonicity is discussed. Finally, some measures of dependence based on the distribution function and on the mean reversed residual life are investigated.Conditional Distribution, Reveserd Hazard Rate, TP2, Dependence Measures

Characterizations of a Class of Distributions by Dual Generalized Order Statistics and Truncated Moments

The problem of characterizing a distribution is an important problem which has recently attracted the attention of many researchers. Thus, various characterizations have been established in many different directions. The present work deals with the characterizations of a general class of distributions. These characterizations are based on: (i) a simple relationship between two truncated moments, (ii) truncated moment of certain functions of the nth order statistic, (iii) single truncated moment of certain functions of the random variable and (iv) moments of dual generalized order statistics.We like to mention that the characterization (i) which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. We also study the recurrence relations between moments of dual generalized order statistics of this class of distributions

The Fisher Information Matrix in Right Censored Data from the Dagum Distribution

In this note, we provide the mathematical details of the calculation of the Fisher information matrix when the data involve type I right censored observations from a Dagum distribution.Fisher information matrix, type I right censored observations, Dagum distribution

THE FISHER INFORMATION MATRIX IN DOUBLY CENSORED DATA FROM THE DAGUM DISTRIBUTION

In this note, we provide the mathematical tools for computing the entries of the Fisher information matrix in case of the observations are doubly censored from a Dagum distribution.Order Statistics, Maximum Likelihood Estimator, Fisher Information Matrix

The “wrong skewness” problem: a re-specification of Stochastic Frontiers.

In this paper, we study the so-called “wrong skewness” anomaly in Stochastic Frontiers (SF), which consists in the observed difference between the expected and estimated sign of the asymmetry of the composite error. We propose a more general and flexible specification of the SF model, introducing dependence between the two error components and asymmetry (positive or negative) of the random error. This re-specification allows us to decompose the third moment of the composite error in three components, namely: i) the asymmetry of the inefficiency term; ii) the asymmetry of the random error; and iii) the structure of dependence between the error components. This decomposition suggests that the “wrong skewness” anomaly is an ill-posed problem, because we cannot establish ex ante the expected sign of the asymmetry of the composite error. We report a relevant special case that allows us to estimate the three components of the asymmetry of the composite error and, consequently, to interpret the estimated sign. We present two empirical applications. In the first dataset, where the classic SF displays wrong skewness, estimation of our model rejects the dependence hypothesis, but accepts the asymmetry of the random error, thus justifying the sign of the skewness of the composite error. In the second dataset, where the classic SF does not display any anomaly, estimation of our model provides evidence of the presence of both dependence between the error components and asymmetry of the random error

On the extreme hydrologic events determinants by means of Beta-Singh-Maddala reparameterization

In previous studies, beta-k distribution and distribution functions strongly related to that, have played important roles in representing extreme events. Among these distributions, the Beta-Singh-Maddala turned out to be adequate for modelling hydrological extreme events. Starting from this distribution, the aim of the paper is to express the model as a function of indexes of hydrological interest and simultaneously investigate on their dependence with a set of explanatory variables in such a way to explore on possible determinants of extreme hydrologic events. Finally, an application to a real hydrologic dataset is considered in order to show the potentiality of the proposed model in describing data and in understanding effects of covariates on frequently adopted hydrological indicators

The “wrong skewness” problem: a re-specification of Stochastic Frontiers.

In this paper, we study the so-called “wrong skewness” anomaly in Stochastic Frontiers (SF), which consists in the observed difference between the expected and estimated sign of the asymmetry of the composite error. We propose a more general and flexible specification of the SF model, introducing dependence between the two error components and asymmetry (positive or negative) of the random error. This re-specification allows us to decompose the third moment of the composite error in three components, namely: i) the asymmetry of the inefficiency term; ii) the asymmetry of the random error; and iii) the structure of dependence between the error components. This decomposition suggests that the “wrong skewness” anomaly is an ill-posed problem, because we cannot establish ex ante the expected sign of the asymmetry of the composite error. We report a relevant special case that allows us to estimate the three components of the asymmetry of the composite error and, consequently, to interpret the estimated sign. We present two empirical applications. In the first dataset, where the classic SF displays wrong skewness, estimation of our model rejects the dependence hypothesis, but accepts the asymmetry of the random error, thus justifying the sign of the skewness of the composite error. In the second dataset, where the classic SF does not display any anomaly, estimation of our model provides evidence of the presence of both dependence between the error components and asymmetry of the random error

The “wrong skewness” problem: a re-specification of Stochastic Frontiers.

In this paper, we study the so-called “wrong skewness” anomaly in Stochastic Frontiers (SF), which consists in the observed difference between the expected and estimated sign of the asymmetry of the composite error. We propose a more general and flexible specification of the SF model, introducing dependence between the two error components and asymmetry (positive or negative) of the random error. This re-specification allows us to decompose the third moment of the composite error in three components, namely: i) the asymmetry of the inefficiency term; ii) the asymmetry of the random error; and iii) the structure of dependence between the error components. This decomposition suggests that the “wrong skewness” anomaly is an ill-posed problem, because we cannot establish ex ante the expected sign of the asymmetry of the composite error. We report a relevant special case that allows us to estimate the three components of the asymmetry of the composite error and, consequently, to interpret the estimated sign. We present two empirical applications. In the first dataset, where the classic SF displays wrong skewness, estimation of our model rejects the dependence hypothesis, but accepts the asymmetry of the random error, thus justifying the sign of the skewness of the composite error. In the second dataset, where the classic SF does not display any anomaly, estimation of our model provides evidence of the presence of both dependence between the error components and asymmetry of the random error