Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach

In this paper, maximum likelihood and Bayes estimators of the parameters, reliability and hazard functions have been obtained for two-parameter bathtub-shaped lifetime distribution when sample is available from progressive Type-II censoring scheme. The Markov chain Monte Carlo (MCMC) method is used to compute the Bayes estimates of the model parameters. It has been assumed that the parameters have gamma priors and they are independently distributed. Gibbs within the Metropolis–Hasting algorithm has been applied to generate MCMC samples from the posterior density function. Based on the generated samples, the Bayes estimates and highest posterior density credible intervals of the unknown parameters as well as reliability and hazard functions have been computed. The results of Bayes estimators are obtained under both the balanced-squared error loss and balanced linear-exponential (BLINEX) loss. Moreover, based on the asymptotic normality of the maximum likelihood estimators the approximate confidence intervals (CIs) are obtained. In order to construct the asymptotic CI of the reliability and hazard functions, we need to find the variance of them, which are approximated by delta and Bootstrap methods. Two real data sets have been analyzed to demonstrate how the proposed methods can be used in practice.     

Circular Binary Block Second- and Higher-Order Neighbor Designs

Some new neighbor designs are presented here. Second-order neighbor designs for different configurations are generated in circular binary blocks. Third-order and fourth-order neighbor designs for some cases are also constructed. In all cases, circular blocks are well separated and these designs are obtained through initial block/s. At the end of the study, some models for analysis of these designs are also presented.     

Minimal circular balanced repeated measurement designs in unequal period sizes

Abstract

Repeated measurement designs (RMDs) are widely used in medicine, pharmacology, animal sciences and psychology. In these fields, there are several situations where these designs should be used in periods of different sizes. With the use of RMD, residual effects or carry over effects may arise and balanced RMDs are solution to this problem. In this article, therefore, some infinite series are developed through method of cyclic shifts to obtain circular balanced repeated measurements designs in periods of two different sizes.     

Optimal design results for 2n factorial paired comparison experiments

Four general classes of partially balanced designs for 2ⁿ factorials, corresponding to four different forms of a general null hypothesis H on factorial effects, are presented. For the typical design in each class, the simplified form of the non-centrality parameter λ² of the asymptotic chi-square distribution of the likelihood ratio statistic for testing the corresponding form of H₀ is derived under defined local alternatives. Optimal designs d₁ maximizing λ² in the i-th class and minimizing the trace, determinant and largest eigenvalue of a defined covariance matrix, i =1,…,4, are determined.     

An extended Gompertz-Makeham distribution with application to lifetime data

In this paper, we propose an extension of the Gompertz-Makeham distribution. This distribution is called the transmuted Gompertz-Makeham (TGM). The new model which can handle bathtub-shaped, increasing, increasing-constant and constant hazard rate functions. This property makes TGM is useful in survival analysis. Various statistical and reliability measures of the model are obtained, including hazard rate function, moments, moment generating function (mgf), quantile function, random number generating, skewness, kurtosis, conditional moments, mean deviations, Bonferroni curve, Lorenz curve, Gini index, mean inactivity time, mean residual lifetime and stochastic ordering; we also obtain the density of the ith order statistic. Estimation of the model parameters is justified by the method of maximum likelihood. An application to real data demonstrates that the TGM distribution can provides a better fit than some other very well known distributions.     

Markov-switching BILINEAR − GARCH models: Structure and estimation

Markov-switching (MS) models are becoming increasingly popular as efficient tools of modeling various phenomena in different disciplines, in particular for non Gaussian time series. In this articlept", we propose a broad class of Markov-switching BILINEAR–GARCH processes (MS ? BLGARCH hereafter) obtained by adding to a MS ? GARCH model one or more interaction components between the observed series and its volatility process. This parameterization offers remarkably rich dynamics and complex behavior for modeling and forecasting financial time-series data which exhibit structural changes. In these models, the parameters of conditional variance are allowed to vary according to some latent time-homogeneous Markov chain with finite state space or “regimes.” The main aim of this new model is to capture asymmetric and hence purported to be able to capture leverage effect characterized by the negativity of the correlation between returns shocks and subsequent shocks in volatility patterns in different regimes. So, first, some basic structural properties of this new model including sufficient conditions ensuring the existence of stationary, causal, ergodic solutions, and moments properties are given. Second, since the second-order structure provides a useful information to identify an appropriate time-series model, we derive the expression of the covariance function of for MS ? BLGARCH and for its powers. As a consequence, we find that the second (resp. higher)-order structure is similar to some linear processes, and hence MS ? BLGARCH (resp. its powers) admit an ARMA representation. This finding allows us for parameter estimation via GMM procedure proved by a Monte Carlo study and applied to foreign exchange rate of the Algerian Dinar against the single European currency.     

Islam and development: opportunities and constraints for Somali women

This article describes the effects of the rise of Islamic extremism on women's lives in Somalia since the early 1990s. Throughout the conflict and afterwards, Somali women's organizations in different parts of the country have been active in both development work and advocacy for peace. They were challenging both the government and nongovernmental organizations to recognize and promote the role of women in society, and to resist threats to women's rights. It has been documented that religious extremists were challenging women's rights within marriage and family, to their economic and political participation outside the home, and to their freedom of dress and behavior. The paper also highlights the fact that wholesome and unwholesome traditional practices tend to be associated with Islam, and with other rights as defined in Islam. It reconfirmed that the violations against Somali women's rights are culturally rooted, and that such practice continues unchecked. Until Somali women received a better education, particularly in religious education, this situation will continue. The only hope are the women's organizations who seriously attempt to redress the extremists' strategy of marginalizing women on the grounds of religious evidence.     

Designs balanced for neighbor effects in circular blocks of size six

The performance of a treatment is affected by the treatments applied to its adjacent plots, especially in the experiments of agriculture, horticulture, forestry, serology and industry. Neighbor designs ensure that treatment comparisons are least affected by neighbor effects, therefore, this is a rich field of investigation in statistics and in combinatorics. In this article, several series of neighbor balanced designs are considered in circular blocks of six units.     

Love of life and death distress: two separate factors

The objectives of the current investigation were threefold: a) to explore the gender differences on love of life (a new construct in the well-being domain) and death distress (death anxiety, death depression, and death obsession); b) to explore the relationship between the scales of these constructs; and c) to examine the factorial structure of these scales. The sample was 245 volunteer Kuwaiti college students (53.5% women). Their mean age was 21.9 (SD = 2.3). They responded to the Love of Life Scale, the Death Anxiety Scale, the Arabic Scale of Death Anxiety, the Death Depression Scale-Revised, and the Death Obsession Scale. Gender differences on love of life were not significant. However, women had significantly higher mean scores for the four death distress scales than did their male counterparts. All the correlations between love of life and the death distress scales were not significant except one pertaining to love of life and death depression (negative) in women. Two oblique factors were extracted: death distress and love of life. It was concluded that these constructs represent two distinct and independent factors. Counselors and clinicians dealing with death distress would find that it is not associated with love of life.     

Estimation and prediction for the generalized inverted exponential distribution based on progressively first-failure-censored data with application

In this paper, the estimation of parameters for a generalized inverted exponential distribution based on the progressively first-failure type-II right-censored sample is studied. An expectation–maximization (EM) algorithm is developed to obtain maximum likelihood estimates of unknown parameters as well as reliability and hazard functions. Using the missing value principle, the Fisher information matrix has been obtained for constructing asymptotic confidence intervals. An exact interval and an exact confidence region for the parameters are also constructed. Bayesian procedures based on Markov Chain Monte Carlo methods have been developed to approximate the posterior distribution of the parameters of interest and in addition to deduce the corresponding credible intervals. The performances of the maximum likelihood and Bayes estimators are compared in terms of their mean-squared errors through the simulation study. Furthermore, Bayes two-sample point and interval predictors are obtained when the future sample is ordinary order statistics. The squared error, linear-exponential and general entropy loss functions have been considered for obtaining the Bayes estimators and predictors. To illustrate the discussed procedures, a set of real data is analyzed.