Exact confidence region for the parameters of the gamma distribution based on two independent samples

The gamma distribution has been discussed by many authors. This article proposes an exact confidence region for the parameters of a two-parameter gamma distribution. The result is based on the fact that the percentiles of the F-distribution, with equal degrees of freedom k, are monotonic in k.     

Parameter estimation for switched counting processes

The paper investigates parameter estimation problems in special Markov modulated counting processes. The events occuring at any state of an underlying Markov chain can be equipped with marks performing additional information on the events. Specifying the model to the case of two-state Markov chain modulation, the so-called switched counting process, some statistical problems are studied:maximum likelihood estimators, Rao-Blackwell optimal estimators, test of equality of the counting intensities of the two states and minimax estimation procedures. Tne consideration could be applied in various practical problems, in particular, in queueing and in reliability models, for example in failure-repair processes with alternatively operating repair systems.     

Point estimation after early stopping in a repeated measures trial

When the individual measurements are statistically independent, the maximum likelihood estimator calculated at the end of a sequential procedure overestimates the underlying effect. There are many clinical trials in which we are interested in comparing changes in responses between two treatment groups sequentially. Lee and DeMets (1991, JASA 86, 757–762) proposed a group sequential method for comparing rates of change when a response variable is measured for eaeh patient at successive follow-up visits. They assumed that the response follows the linear mixed effects model and derived the asymptotic joint distribution of the sequentially computed statistics. In this article, we consider the maximum likelihood estimator (MLE), the median unbiased estimator (MUE) and the midpoint of a 100(1-α)% confidence interval as point estimators for the rate of change in the linear mixed effects model, and investigate their properties by Monte Carlo simulation.     

A generalized two-piece skew normal distribution and some of its properties

In this paper, we develop a generalized version of the two-piece skew normal distribution of Kim [On a class of two-piece skew-normal distributions, Statistics 39(6) (2005), pp. 537–553] and derive explicit expressions for its distribution function and characteristic function and discuss some of its important properties. Further estimation of the parameters of the generalized distribution is carried out.     

Bayes sequential estimation for a Poisson process under a LINEX loss function

In this paper, within the framework of a Bayesian model, we consider the problem of sequentially estimating the intensity parameter of a homogeneous Poisson process with a linear exponential (LINEX) loss function and a fixed cost per unit time. An asymptotically pointwise optimal (APO) rule is proposed. It is shown to be asymptotically optimal for the arbitrary priors and asymptotically non-deficient for the conjugate priors in a similar sense of Bickel and Yahav [Asymptotically pointwise optimal procedures in sequential analysis, in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, University of California Press, Berkeley, CA, 1967, pp. 401–413; Asymptotically optimal Bayes and minimax procedures in sequential estimation, Ann. Math. Statist. 39 (1968), pp. 442–456] and Woodroofe [A.P.O. rules are asymptotically non-deficient for estimation with squared error loss, Z. Wahrsch. verw. Gebiete 58 (1981), pp. 331–341], respectively. The proposed APO rule is illustrated using a real data set.     

Hypothesis test for paired samples in the presence of missing data

Missing data are present in almost all statistical analysis. In simple paired design tests, when some subject has one of the involved variables missing in the so-called partially overlapping samples scheme, it is usually discarded for the analysis. The lack of consistency between the information reported in the univariate and multivariate analysis is, perhaps, the main consequence. Although the randomness on the missing mechanism (missingness completely at random) is an usual and needed assumption for this particular situation, missing data presence could lead to serious inconsistencies on the reported conclusions. In this paper, the authors develop a simple and direct procedure which allows using the whole available information in order to perform paired tests. In particular, the proposed methodology is applied to check the equality among the means from two paired samples. In addition, the use of two different resampling techniques is also explored. Finally, real-world data are analysed.     

A Practical Implementation and Bayesian Estimation in Franklin's Randomized Response Procedure

A Bayesian estimator based on Franklin's randomized response procedure is proposed for proportion estimation in surveys dealing with a sensitive character. The method is simple to implement and avoids the usual drawbacks of Franklin's estimator, i.e., the occurrence of negative estimates when the population proportion is small. A simulation study is considered in order to assess the performance of the proposed estimator as well as the corresponding credible interval.     

An Exponential Model for Damage Accumulation

In this article, we present a general model for predicting the fatigue behavior for any stress level and amplitude using the exponential model. Based on the Wöhler field for fixed stress level, a compatibility functional equation enables us to derive the general model with eight parameters. The problem of parameter estimation is then discussed and some methods are described. Some examples are finally presented to illustrate the derived model and the proposed methods of estimation.     

基于理想解和灰关联度的动态评价方法及其应用研究

为了对多个多属性（指标）待评价对象（方案）在多个时间点的发展状态和该时间段内的总体发展水平进行比较分析，根据理想解法和灰关联度法优缺点，提出基于理想解和灰关联度的动态评价方法。该方法基于三维数据，将欧氏距离和灰色关联度相结合，提出一种新贴近度，同时反映了位置关系和数据曲线的相似性差异，兼顾评价指标值差异程度和增长程度。最后将该方法应用于"十二五"期间省域循环经济生态效益评价，通过实例验证该方法实际应用上的有效性。