On finite mixture of two-component gompertz lifetime model

The Gompertz distribution has been used as a growth model, especially in epidemiological and biomedical studies. Based on Type I and II censored samples from a heterogeneous population that can be represented by a finite mixture of two-component Gompertz lifetime model, the maximum likelihood and Bayes estimates of the parameters, reliability and hazard rate functions are obtained. An approximation form due to Lindley (1980) is used in obtaining the corresponding Bayes estimates. The maximum likelihood and Bayes estimates are comparedvia a Monte Carlo simulation study.     

Inference and prediction for pareto progressively censored data

Progressively censored data from a classical Pareto distribution are to be used to make inferences about its shape and precision parameters and the reliability function. An approximation form due to Tierney and Kadane (1986) is used for obtaining the Bayes estimates. Bayesian prediction of further observations from this distribution is also considered. When the Bayesian approach is concerned, conjugate priors for either the one or the two parameters cases are considered. To illustrate the given procedures, a numerical example and a simulation study are given.     

Bias reduction for the ratio of means

Confidence intervals of third-order accuracy are given for the ratio of the means of two normal distributions. A simulation study is conducted to compare these intervals with ones known. A comparison is also made with non-parametric alternatives.     

Closed-form approximate tolerance intervals for some general linear models and comparison studies

The problems of constructing tolerance intervals (TIs) in random effects model and in a mixed linear model are considered. The methods based on the generalized variable (GV) approach and the one based on the modified large sample (MLS) procedure are evaluated with respect to coverage probabilities and expected width in various setups using Monte Carlo simulation. Our comparison studies indicate that the TIs based on the MLS procedure are comparable to or better than those based on the GV approach. As the MLS TIs are in closed-form, they are easier to compute than those based on the GV approach. TIs for a two-way nested model are also derived using the MLS method, and their merits are evaluated using simulation. The procedures are illustrated using a practical example.     

A Bayesian structural-change analysis via the stochastic approximation Monte Carlo and Gibbs sampler

In this article, we propose a Bayesian approach to estimate the multiple structural change-points in a level and the trend when the number of change-points is unknown. Our formulation of the structural-change model involves a binary discrete variable that indicates the structural change. The determination of the number and the form of structural changes are considered as a model selection issue in Bayesian structural-change analysis. We apply an advanced Monte Carlo algorithm, the stochastic approximation Monte Carlo (SAMC) algorithm, to this structural-change model selection issue. SAMC effectively functions for the complex structural-change model estimation, since it prevents entrapment in local posterior mode. The estimation of the model parameters in each regime is made using the Gibbs sampler after each change-point is detected. The performance of our proposed method has been investigated on simulated and real data sets, a long time series of US real gross domestic product, US uses of force between 1870 and 1994 and 1-year time series of temperature in Seoul, South Korea.     

Bayesian and maximum likelihood estimations of the inverse Weibull parameters under progressive type-II censoring

In this paper, the statistical inference of the unknown parameters of a two-parameter inverse Weibull (IW) distribution based on the progressive type-II censored sample has been considered. The maximum likelihood estimators (MLEs) cannot be obtained in explicit forms, hence the approximate MLEs are proposed, which are in explicit forms. The Bayes and generalized Bayes estimators for the IW parameters and the reliability function based on the squared error and Linex loss functions are provided. The Bayes and generalized Bayes estimators cannot be obtained explicitly, hence Lindley's approximation is used to obtain the Bayes and generalized Bayes estimators. Furthermore, the highest posterior density credible intervals of the unknown parameters based on Gibbs sampling technique are computed, and using an optimality criterion the optimal censoring scheme has been suggested. Simulation experiments are performed to see the effectiveness of the different estimators. Finally, two data sets have been analysed for illustrative purposes.     

Confidence sets based on the positive part James–Stein estimator with the asymptotically constant coverage probability

The asymptotic expansions for the coverage probability of a confidence set centred at the James–Stein estimator presented in our previous publications show that this probability depends on the non-centrality parameter τ² (the sum of the squares of the means of normal distributions). In this paper we establish how these expansions can be used for a construction of confidence region with constant confidence level, which is asymptotically (the same formula for both case τ→0 and τ→∞) equal to some fixed value 1?α. We establish the shrinkage rate for the confidence region according to the growth of the dimension p and also the value of τ for which we observe quick decreasing of the coverage probability to the nominal level 1?α. When p→∞ this value of τ increases as O(p^1/4). The accuracy of the results obtained is shown by the Monte-Carlo statistical simulations.     

A control chart using an auxiliary variable and repetitive sampling for monitoring process mean

In this paper, a new control chart is proposed by using an auxiliary variable and repetitive sampling in order to enhance the performance of detecting a shift in process mean. The product-difference type estimator of the mean is plotted on the proposed control chart, which utilizes the information of an auxiliary variable correlated with the main quality variable. The proposed control chart is based on the outer and inner control limits so that repetitive sampling is allowed when the plotted statistic falls between the two limits. The average run length (ARL) of the proposed control chart is evaluated using the Monte Carlo simulation. The proposed control chart is compared with the Riaz M control chart and the results show the outperformance of the proposed control chart in terms of the ARL.     

Mean-shift outliers model in skew scale-mixtures of normal distributions

ABSTRACT

Asymmetric models have been discussed quite extensively in recent years, in situations where the normality assumption is suspected due to lack of symmetry in the data. Techniques for assessing the quality of fit and diagnostic analysis are important for model validation. This paper presents a study of the mean-shift method for the detection of outliers in regression models under skew scale-mixtures of normal distributions. Analytical solutions for the estimators of the parameters are obtained through the use of Expectation–Maximization algorithm. The observed information matrix for the calculation of standard errors is obtained for each distribution. Simulation studies and an application to the analysis of a data have been carried out, showing the efficiency of the proposed method in detecting outliers.     

Asymptotic efficiencies of estiamtors of location a comutational study

Asymptotic efficiencies of four classes of estimators of location are evaluated for a family of distributions consisting of t, lambda and contaminated normal densities. For the class of estimators derived from signed rank tests, maximin efficiencies between pairs of distributions in the family are computed using a formula of Gastwirth ( 1966 ). Asymptotic efficiencies are also evaluated for the scale dependent estimators of the form proposed by Hubcr ( 1964 ) and the efficiencies of procedures utilizing interquantiie ranges.are evaluated. Efficiencies of linear estimators such as trimmed means, BLUE's for the lambda family are computed for each density considered. Efficiencies of linear, polynomial and trigonometric approximations to BLUE weight functions are determined. Using the method of Birnbaum and Laska ( 1967 ) maximin efficiencies are computed using four linear or polynomial terms. On the basis of comparisons of these numerical results, suggestions for robust estimators are given