Approximate Bayes estimation of the parameters and reliability function of a mixture of two inverse Weibull distributions under Type-2 censoring

The main goal of this paper is to develop the approximate Bayes estimation of the five-dimensional vector of the parameters and reliability function of a mixture of two inverse Weibull distributions (MTIWD) under Type-2 censoring. Usually, the posterior distribution is complicated under the scheme of Type-2 censoring and the integrals that are involved cannot be obtained in a simple explicit form. In this study, we use Lindley's [Approximate Bayesian method, Trabajos Estadist. 31 (1980), pp. 223–237] approximate form of Bayes estimation in the case of an MTIWD under Type-2 censoring. Later, we calculate the estimated risks (ERs) of the Bayes estimates and compare them with the corresponding ERs of the maximum-likelihood estimates through Monte Carlo simulation. Finally, we analyse a real data set using the findings.     

Comparing the relative efficiency of three sequential procedures

We consider the sequential procedures developed by Robbins and Siegmund (1974), Louis (1975) and Zoubeidi (1992) for comparing the means of two treatments. We let the procedures have equal power functions and compare their Bayes and minimax risks using the invariance property of their power functions. For each of several formulations of the problem we determine the most relatively efficient procedure and compute its expected total sample size.     

The umvue and bayes estimate of reliability of mixed failure time distribution

We study the reliability estimates of the non-standard mixture of degenerate (degenerated at zero) and exponential distributions. The Uniformly Minimum Variance Unbiased Estimator (UMVUE) and Bayes estimator of the reliability for some selective prior when the mixing proportion is known and unknown are derived. The Bayes risk is computed for each Bayes estimator of the reliability. A simulated study is carried out to assess the performance of the estimators alongwith the true and Maximum Likelihood Estimate (MLE) of the reliability. An example from Vannman (1991) is also discussed at the end of the paper.     

Optimum Critical Value for Pre-Test Estimator

In this paper, methods are proposed in finding the robust design in both Taguchi and Standard setups when a signal factor is present. The robust design is a set of level combinations of control factors so that the effect of controllable noise factors on response is minimum. Both univariate and multivariate methods are used in finding the influential noise factors for the determination of robust designs.     

Serials Clutter in Online Catalogs

Abstract

Finding and deciphering serials records in online catalogs is a challenge to many library users. To understand and analyze these challenges, the author conducted searches for scientific journal titles in the online catalogs of Committee on Institutional Cooperation (CIC) libraries. The first part of the study measures the difficulty of retrieving serial records from online catalogs comparing one-word versus multiple-word titles. The second part analyzes displays for complexity by measuring the length of the complete record and the length of the holdings statements. These data show the complexity of displays and indicate the potential confusion that these displays may induce in library users.     

Simple Formulae for Evaluating the Potential Impact of Confounding Bias

Unmeasured confounding is a common problem in observational studies. This article presents simple formulae that can set the bounds of the confounding risk ratio under three standard populations of the exposed, unexposed, and total groups. The bounds are derived by considering the confounding risk ratio as a function of the prevalence of a covariate, and can be constructed using only information about either the exposure–confounder or the disease–confounder relationship. The formulae can be extended to the confounding odds ratio in case–control studies, and the confounding risk difference is discussed. The application of these formulae is demonstrated using an example in which estimation may suffer from bias due to population stratification. The formulae can help to provide a realistic picture of the potential impact of bias due to confounding.     

Two-Stage Variables Acceptance Sampling Plans Using Process Loss Functions

In this article, a variable two-stage acceptance sampling plan is developed when the quality characteristic is evaluated through a process loss function. The plan parameters of the proposed plan are determined by using the two-point approach and tabulated according to various quality levels. Two cases are discussed when the process mean lies at the target value and when it does not, respectively. Extensive tables are provided for both cases and the results are explained with examples. The advantage of the proposed plan is compared with the existing variable single acceptance sampling plan using the process loss function.     

First- and Second-order Asymptotics for the Tail Distortion Risk Measure of Extreme Risks

The tail distortion risk measure at level p was first introduced in Zhu and Li (2012 Zhu, L., Li, H. (2012). Tail distortion risk and its asymptotic analysis. Insur. Math. Econ. 51(1):115–121.[Crossref], [Web of Science ®] , [Google Scholar]), where the parameter p ∈ (0, 1) indicates the confidence level. They established first-order asymptotics for this risk measure, as p↑1, for the Fréchet case. In this article, we extend their work by establishing both first-order and second-order asymptotics for the Fréchet, Weibull, and Gumbel cases. Numerical studies are also carried out to examine the accuracy of both asymptotics.     

Bimodal skew-symmetric normal distribution

ABSTRACT

We introduce a new parsimonious bimodal distribution, referred to as the bimodal skew-symmetric Normal (BSSN) distribution, which is potentially effective in capturing bimodality, excess kurtosis, and skewness. Explicit expressions for the moment-generating function, mean, variance, skewness, and excess kurtosis were derived. The shape properties of the proposed distribution were investigated in regard to skewness, kurtosis, and bimodality. Maximum likelihood estimation was considered and an expression for the observed information matrix was provided. Illustrative examples using medical and financial data as well as simulated data from a mixture of normal distributions were worked.     

Uniform asymptotics for ruin probability of a two-dimensional dependent renewal risk model

ABSTRACT

In this paper we consider the tail behavior of a two-dimensional dependent renewal risk model with two dependent classes of insurance business, in which the claim sizes are governed by a common renewal counting process, and their inter-arrival times are dependent, identically distributed. For the case that the claim size distribution belongs to the intersection of long-tailed distribution class and dominant variation class, we obtain an asymptotic formula, which holds uniformly for all time in an infinite interval. Moreover, we point out that the formula still holds uniformly for all time in an infinite interval for widely dependent random variables (r.v.s) under some conditions.