Slashed generalized Rayleigh distribution

We introduce a new family of distributions suitable for fitting positive data sets with high kurtosis which is called the Slashed Generalized Rayleigh Distribution. This distribution arises as the quotient of two independent random variables, one being a generalized Rayleigh distribution in the numerator and the other a power of the uniform distribution in the denominator. We present properties and carry out estimation of the model parameters by moment and maximum likelihood (ML) methods. Finally, we conduct a small simulation study to evaluate the performance of ML estimators and analyze real data sets to illustrate the usefulness of the new model.     

Ignorability conditions for frequentist non parametric analysis of conditional distributions with incomplete data

Rubin (1976 Rubin, D.B. (1976). Inference and missing data. Biometrika 63(3):581–592.[Crossref], [Web of Science ®] , [Google Scholar]) derived general conditions under which inferences that ignore missing data are valid. These conditions are sufficient but not generally necessary, and therefore may be relaxed in some special cases. We consider here the case of frequentist estimation of a conditional cdf subject to missing outcomes. We partition a set of data into outcome, conditioning, and latent variables, all of which potentially affect the probability of a missing response. We describe sufficient conditions under which a complete-case estimate of the conditional cdf of the outcome given the conditioning variable is unbiased. We use simulations on a renal transplant data set (Dienemann et al.) to illustrate the implications of these results.     

Gamma-Maxwell distribution

A new two-parameter distribution, the gamma-Maxwell distribution, isproposed and studied. We generate the new distribution using the gamma-G generator of distributions. The proposal distribution can be seen as an extension of the Maxwell distribution with more flexibility in terms of the distribution asymmetry and kurtosis. We study some probability properties, discuss maximum-likelihood estimation and present a real data application indicating that the new distribution can improve the ordinary Maxwell distribution in fitting real data.     

Estimation of parameters of inverse Weibull distribution and application to multi-component stress-strength model

The problem of estimation of the parameters of two-parameter inverse Weibull distributions has been considered. We establish existence and uniqueness of the maximum likelihood estimators of the scale and shape parameters. We derive Bayes estimators of the parameters under the entropy loss function. Hierarchical Bayes estimator, equivariant estimator and a class of minimax estimators are derived when shape parameter is known. Ordered Bayes estimators using information about second population are also derived. We investigate the reliability of multi-component stress-strength model using classical and Bayesian approaches. Risk comparison of the classical and Bayes estimators is done using Monte Carlo simulations. Applications of the proposed estimators are shown using real data sets.     

Estimation of system reliability for exponential distributions based on L ranked set sampling

Abstract

In the case where strength and stress both follow exponential distributions, this paper considers the maximum likelihood estimator (MLE) of the system reliability based on L ranked set sampling (LRSS). The proposed MLE is shown to have existence, uniqueness and asymptotic normality, and its asymptotic variance is obtained by the Fisher information matrix of LRSS. The values of asymptotic relative efficiencies show that the proposed MLE is always more efficient than the MLE using simple random sampling (SRS). However, the MLE using LRSS cannot be written in closed form. Therefore, the modified MLE is proposed using the technique replaced some terms in the maximum likelihood equations by their expectations. The newly modified MLE using LRSS is shown to be superior to the MLE using SRS. Finally, the proposed method is applied to a real data set on metastatic renal carcinoma study.     

A non‐stationary bivariate INAR(1) process with a simple cross‐dependence: Estimation with some properties

This paper considers modelling of a non‐stationary bivariate integer‐valued autoregressive process of order 1 (BINAR(1)) where the cross‐dependence between the counting series is formed through the relationship of the current series with the previous‐lagged count series observations while the pair of innovations is independent and marginally Poisson. In addition, this paper proposes a generalised quasi‐likelihood (GQL) estimating equation based on the exact specification of the mean score and the auto‐covariance structure. The proposed approach is also compared with other popular techniques such as conditional maximum likelihood (CML), generalised least squares (GLS) and generalised method of moment (GMM) based on simulated data from the proposed BINAR(1). Moreover, the model is applied to weekly series of day and night road accidents arising in some regions of Mauritius and is compared with other existing BINAR(1) models.     

分支蚁群动态扰动算法求解TSP问题

蚁群优化算法是一种求解组合优化难题的强启发式算法,它利用正反馈和并行计算原理,具备很强的搜索能力。近年来,蚁群优化算法广泛应用于TSP问题的研究。本文提出分支蚁群动态扰动(DPBAC)算法,该算法主要从5个方面对基本蚁群算法做出改进:引入分支策略选取出发城市;改进状态转移规则;引入变异策略改进蚂蚁路径;改进信息素更新规则;引入条件动态扰动策略。实验表明,该算法可以有效改善基本蚁群算法搜索时间较长、容易陷入局部极小等缺点。     

Nonparametric Tests for Stratum Effects in the Cox Model

Thispaper considers the stratified proportional hazards model witha focus on the assessment of stratum effects. The assessmentof such effects is often of interest, for example, in clinicaltrials. In this case, two relevant tests are the test of stratuminteraction with covariates and the test of stratum interactionwith baseline hazard functions. For the test of stratum interactionwith covariates, one can use the partial likelihood method (Kalbfleischand Prentice, 1980; Lin, 1994). For the test of stratum interactionwith baseline hazard functions, however, there seems to be noformal test available. We consider this problem and propose aclass of nonparametric tests. The asymptotic distributions ofthe tests are derived using the martingale theory. The proposedtests can also be used for survival comparisons which need tobe adjusted for covariate effects. The method is illustratedwith data from a lung cancer clinical trial.     

China’s GDP: Examining provincial disparities (1952–1998)

Accompanying rapid economic growth in China, there have been provincial disparities. This article presents and analyzes the evolution of Chinas provincial GDP per capita disparity between 1952 and 1998. First, an examination of some basic indicators of disparity is carried out, and a test for unconditional convergence is performed to explore the dispersion features. Then, a more comprehensive regression analysis, allowing insights into the evidence of conditional convergence and highlighting the main determinants of growth in two main periods of the recent history of China (i.e., prereform and postreform) is presented. Finally, a discussion and conclusion are provided.