An extended Birnbaum–Saunders distribution: Theory,estimation, and applications

Abstract

Birnbaum and Saunders (1969a Birnbaum, Z.W., Saunders, S.C. (1969a). A new family of life distributions. J. Appl. Probab. 6:319–327.[Crossref], [Web of Science ®] , [Google Scholar]) pioneered a lifetime model which is commonly used in reliability studies. Based on this distribution, a new model called the gamma Birnbaum–Saunders distribution is proposed for describing fatigue life data. Several properties of the new distribution including explicit expressions for the ordinary and incomplete moments, generating and quantile functions, mean deviations, density function of the order statistics, and their moments are derived. We discuss the method of maximum likelihood and a Bayesian approach to estimate the model parameters. The superiority of the new model is illustrated by means of three failure real data sets. We also propose a new extended regression model based on the logarithm of the new distribution. The last model can be very useful to the analysis of real data and provide more realistic fits than other special regression models.     

A note on influence diagnostics in AR(1) time series models

The purpose of this paper is to develop influence diagnostics for AR(1) models under the innovative and the data perturbation schemes. There are four main contributions. First, we derive analytical expressions for the slope and curvature statistics. Second, we establish a relationship between the slope and curvature showing that the standardised slope and standardised curvature are equal for the innovative perturbation scheme, and these vectors are nearly identical for several values of the autoregressive parameter, for the data perturbation scheme. Third, we present a connection between the influence statistics and the tests for outlier detection. Fourth, for the innovative perturbation scheme, we derive the asymptotic distribution of a new influence statistic, whereas for the data perturbation scheme, the distribution of the influence statistics is obtained via Monte Carlo simulation. We additionally discuss practical guidelines for the use of local influence statistics, which are illustrated on a chemical process data set.     

A longitudinal perspective on the differentiated valuation of formal education in Brazil in recent decades

The central theme of this article is the relationship between formal education and earnings from a longitudinal perspective, taking into account indicators of social status. Variations in the respective trajectories, in different age cohorts, and in the comparison among different periods are discussed. The empirical material used is based on the microdata files of official statistics. The main techniques put into practice are those that are most focused on measuring the degree of interdependence among variables and those used for means comparison. Our general hypothesis is that the effects of schooling cannot be grasped in terms of education itself but instead in terms of its relationship to status in the social and power structures. One of this paper's principal observations is that of the general declining trend in the economic value of formal education, which varies depending on the level of education and social status. This devaluation is systematic and spans the entire studied universe; however, it focuses much more closely on those of lower social status, particularly for the groups with schooling that is either higher or lower than average.     

Oil and gas depletion: Diffusion models and forecasting under strategic intervention

Crude oil and natural gas depletion may be modelled by a diffusion process based upon a constrained life-cycle. Here we consider the Generalized Bass Model. The choice is motivated by the realistic assumption that there is a self-evident link between oil and gas extraction and the spreading of the modern technologies in wide areas such as transport, heating, cooling, chemistry and hydrocarbon fuels consumption. Such a model may include deterministic or semi-deterministic regulatory interventions. Statistical analysis is based upon nonlinear methodologies and more flexible autoregressive structure of residuals. The technical aim of this paper is to outline the meaningful hierarchy existing among the components of such diffusion models. Statistical effort in residual component analysis may be read as a significant confirmation of a well-founded diffusion process under rare but strong deterministic shocks. Applications of such ideas are proposed with reference to world oil and gas production data and to particular regions such as mainland U.S.A., U.K., Norway and Alaska. The main results give new evidence in time-peaks location and in residual times to depletion.     

GMC/GEL estimation of stochastic volatility models

In this article we discuss the estimation of stochastic volatility (SV) using generalized empirical likelihood/minimum contrast methods based on moment conditionsmodels. We show via Monte Carlo simulations that the proposed methods have superior or equivalent performance to the other alternative methods, and, additionally, they offer robustness properties in the presence of heavy-tailed distributions and outliers.     

The inverse weighted Lindley distribution: Properties,estimation and an application on a failure time data

In this paper a new distribution is proposed. This new model provides more flexibility to modeling data with upside-down bathtub hazard rate function. A significant account of mathematical properties of the new distribution is presented. The maximum likelihood estimators for the parameters in the presence of complete and censored data are presented. Two corrective approaches are considered to derive modified estimators that are bias-free to second order. A numerical simulation is carried out to examine the efficiency of the bias correction. Finally, an application using a real data set is presented in order to illustrate our proposed distribution.     

A strange tale

We are going through such challenging times that dealing with reality is sometimes easier through fiction. Therefore, we tell the tale of a faraway land where poor women — mostly black — who make a living as domestic servants are particularly impacted by the COVID‐19 pandemic. Their abject bodies are part of a form of necropolitics that separates those who must live from those who can die. Their bodies do not matter, as they are perceived as mere working tools. And what sounds like a strange tale is the true reality of millions of women during the pandemic, in a land that is not so far away as it seems.     

Restricted alternatives tests in a bivariate exponential model with covariates

This paper is about the analysis of paired survival data using the exponential bivariate model of Sarkar for the underlying survival times, (X,Y), subject to censoring. Under this parametric model we test parameters in the presence of covariates. We consider first, tests of hypotheses of independence and equality of survival marginals, and second, test of hypotheses of covariate effects and survival superiority of one marginal over the other are considered. For this last question we applied a statistical test based on the Union-intersection principle.     

Linear calibration in functional regression models

This paper discusses calibration in functional regression models. Classical and inverse type estimators are considered. First order approximation to the bias and to the mean squared error (MSE) of the estimators are considered. Numerical comparisons seem to indicate that the classical estimator obtained via maximum likelihood estimation performs better than the other estimators considered.