A likelihood ratio test to discriminate exponential–Poisson and gamma distributions

The exponential–Poisson (EP) distribution with scale and shape parameters β>0 and λ∈?, respectively, is a lifetime distribution obtained by mixing exponential and zero-truncated Poisson models. The EP distribution has been a good alternative to the gamma distribution for modelling lifetime, reliability and time intervals of successive natural disasters. Both EP and gamma distributions have some similarities and properties in common, for example, their densities may be strictly decreasing or unimodal, and their hazard rate functions may be decreasing, increasing or constant depending on their shape parameters. On the other hand, the EP distribution has several interesting applications based on stochastic representations involving maximum and minimum of iid exponential variables (with random sample size) which make it of distinguishable scientific importance from the gamma distribution. Given the similarities and different scientific relevance between these models, one question of interest is how to discriminate them. With this in mind, we propose a likelihood ratio test based on Cox's statistic to discriminate the EP and gamma distributions. The asymptotic distribution of the normalized logarithm of the ratio of the maximized likelihoods under two null hypotheses – data come from EP or gamma distributions – is provided. With this, we obtain the probabilities of correct selection. Hence, we propose to choose the model that maximizes the probability of correct selection (PCS). We also determinate the minimum sample size required to discriminate the EP and gamma distributions when the PCS and a given tolerance level based on some distance are before stated. A simulation study to evaluate the accuracy of the asymptotic probabilities of correct selection is also presented. The paper is motivated by two applications to real data sets.     

关注大学生就业问题,谋求地方高师院校长足发展

通过对地方高师院校毕业生就业形势的深入分析,剖析了引发地方高师院校毕业生就业难的内因和外因。从学校长足发展的角度,对地方高师院校的教育、管理和服务提出了改进措施。     

Reliability of stress–strength model for exponentiated Pareto distributions

In this paper, the reliability of a system is discussed when the strength of the system and the stress imposed on it are independent, non-identical exponentiated Pareto distributed random variables. Different point estimations and interval estimations are proposed. The point estimators obtained are maximum likelihood, uniformly minimum variance unbiased and Bayesian estimators. The interval estimations obtained are approximate, exact, bootstrap-p and bootstrap-t confidence intervals and Bayesian credible interval. Different methods and the corresponding confidence intervals are compared using Monte-carlo simulations.     

The labour market flexibility debate in India: Re‐examining the case for signing voluntary contracts

A major focus of India's ongoing policy debate over labour market flexibilization has been the statutory requirement that firms employing 100 or more workers cannot dismiss employees without prior government permission. The case for repealing that requirement (or greatly increasing the workforce threshold) is notably underpinned by Basu, Fields and Debgupta (2009). Here, the author challenges their particular theoretical argument for hiring and firing at will based on the voluntary signing of contracts, demonstrating that their general policy conclusion is logically unsustainable even within the framework of that model. The case for labour market flexibilization through voluntary contracting thus remains unfounded.     

Prediction intervals for future Weibull residual data

In reliability theory, risk analysis, renewal processes and actuarial studies, the residual lifetimes data play an important essential role in studying the conditional tail of the lifetime data. In this paper, based on some observed ordered residual Weibull data, we introduce different prediction methods for obtaining prediction intervals (PIs) of future residual lifetimes including likelihood, Wald, moments, parametric bootstrap, and highest conditional methods. Monte Carlo simulations are performed to compare the performances of the so obtained PIs and one data analysis is performed for illustration purposes.     

A new generalization of alpha-skew-normal distribution

In this paper, a new generalization of alpha-skew-normal distribution is considered. Some properties of this distribution, which is denoted by GASN(α, λ), including moments, maximum likelihood estimation of parameters, and some other properties are studied. Finally, using a real data set, we show that our new distribution is the best-fitted distribution for the used data among normal, skew normal, alpha-skew-normal, and skew-bimodal-normal distributions.     

The empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior under Stein's loss function

For the hierarchical Poisson and gamma model, we calculate the Bayes posterior estimator of the parameter of the Poisson distribution under Stein's loss function which penalizes gross overestimation and gross underestimation equally and the corresponding Posterior Expected Stein's Loss (PESL). We also obtain the Bayes posterior estimator of the parameter under the squared error loss and the corresponding PESL. Moreover, we obtain the empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior by two methods. In numerical simulations, we have illustrated: The two inequalities of the Bayes posterior estimators and the PESLs; the moment estimators and the Maximum Likelihood Estimators (MLEs) are consistent estimators of the hyperparameters; the goodness-of-fit of the model to the simulated data. The numerical results indicate that the MLEs are better than the moment estimators when estimating the hyperparameters. Finally, we exploit the attendance data on 314 high school juniors from two urban high schools to illustrate our theoretical studies.     

Asymptotic approximations to the distribution of Kendall's sample τ

This paper provides a saddlepoint approximation to the distribution of the sample version of Kendall's τ, which is a measure of association between two samples. The saddlepoint approximation is compared with the Edgeworth and the normal approximations, and with the bootstrap resampling distribution. A numerical study shows that with small sample sizes the saddlepoint approximation outperforms both the normal and the Edgeworth approximations. This paper gives also an analytical comparison between approximated and exact cumulants of the sample Kendall's τ when the two samples are independent.     

Reliability analysis of systems with components having two dependent subcomponents

In this article, a system that consists of n independent components each having two dependent subcomponents (A_i, B_i), i = 1, …, n is considered. The system is assumed to compose of components that have two correlated subcomponents (A_i, B_i), and functions iff both systems of subcomponents A₁, A₂, …, A_n and B₁, B₂, …, B_n work under certain structural rules. The expressions for reliability and mean time to failure of such systems are obtained. A sufficient condition to compare two systems of bivariate components in terms of stochastic ordering is also presented.