Normal approximation in an urn model with indistinguishable balls

For the Bose-Einstein Statistics, where n indistinguishable balls are distributed in m urns such that all the arrangements are equally likely, define the random variables

M_k = number of urns containing exactly k balls each;

N_k = number of urns containing at least k balls each.

We consider the approximation of the distributions of M_k and N_k by suitable normal distributions, for large but finite m. Estimates are found for the error in the approximation to both the probability mass function and the distribution function in each case. These results apply also to the alternative model where no urn is allowed to be empty. The results are illustrated by some numerical examples.     

Model-based confidence bands for survival functions

This paper focuses on a novel method of developing one-sample confidence bands for survival functions from right censored data. The approach is model-based, relying on a parametric model for the conditional expectation of the censoring indicator given the observed minimum, and derives its strength from easy access to a good-fitting model among a plethora of choices available for binary response data. The substantive methodological contribution is in exploiting a semiparametric estimator of the survival function to produce improved simultaneous confidence bands. To obtain critical values for computing the confidence bands, a two-stage bootstrap approach that combines the classical bootstrap with the more recent model-based regeneration of censoring indicators is proposed and a justification of its asymptotic validity is also provided. Several different confidence bands are studied using the proposed approach. Numerical studies, including robustness of the proposed bands to misspecification, are carried out to check efficacy. The method is illustrated using two lung cancer data sets.     

The Modified Pulak and Al-Sultan's Model for Determining the Optimum Process Parameters

Economic selection of process parameters has been an important topic in modern statistical process control. The optimum process parameters setting have a major effect on the expected profit/cost per item. There are some concerns on the problem of setting process parameters. Boucher and Jafari (1991 Boucher , T. O. , Jafari , M. A. ( 1991 ). The optimum target value for single filling operations with quality sampling plans . J. Qual. Technol. 23 : 44 – 47 . [CSA] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) first considered the attribute single sampling plan applied in the selection of process target. Pulak and Al-Sultan (1996 Pulak , M. F. S. , Al-Sultan , K. S. ( 1996 ). The optimum targeting for a single filling operation with rectifying inspection . Omega 24 : 727 – 733 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) extended Boucher and Jafari's model and presented the rectifying inspection plan for determining the optimum process mean. In this article, we further propose a modified Pulak and Al-Sultan model for determining the optimum process mean and standard deviation under the rectifying inspection plan with the average outgoing quality limit (AOQL) protection. Taguchi's (1986 Taguchi , G. ( 1986 ). Introduction to Quality Engineering . Asian Productivity Organization . [Google Scholar]) symmetric quadratic quality loss function is adopted for evaluating the product quality. By solving the modified model, we can obtain the optimum process parameters with the maximum expected profit per item and the specified quality level can be reached.     

On Upshifted Reversed Mean Residual Life Order

Recently, the concept of reversed mean residual life order based on the mean of the random variable X _t  = (t ? X | X ≤ t), t > 0, called the reversed residual life, defined for the nonnegative random variable X, has been introduced in the literature. In this paper, a stochastic order based on the shifted version of the reversed mean residual life is proposed, based on the reversed mean residual life function for a random variable X with support (l _X , ∞), where l _X may be negative infinity, and its properties are studied. Closure under the Poisson shock model and properties for spare allocation are also discussed.     

Multivariate Kendall's tau for change‐point detection in copulas

Statistical procedures for the detection of a change in the dependence structure of a series of multivariate observations are studied in this work. The test statistics that are proposed are $L_1$ , $L_2$ , and $L_{\infty }$ distances computed from vectors of differences of Kendall's tau; two multivariate extensions of Kendall's measure of association are used. Since the distributions of these statistics under the null hypothesis of no change depend on the unknown underlying copula of the vectors, a procedure based on the multiplier central limit theorem is used for the computation of p‐values; the method is shown to be valid both asymptotically and for moderate sample sizes. Alternative versions of the tests that take into account possible breakpoints in the marginal distributions are also investigated. Monte Carlo simulations show that the tests are powerful under many scenarios of change‐point. In addition, two estimators of the time of change are proposed and their efficiency is carefully studied. The methodologies are illustrated on simulated series from the Canadian Regional Climate Model. The Canadian Journal of Statistics 41: 65–82; 2013 © 2012 Statistical Society of Canada     

Number of observations near the maximum in an F α-scheme

Let K _n (a) be the number of observations in the interval (M _n ,?a, M _n ), where M _n is the maximum value in a sequence of size n. We study the asymptotic properties of K _n (a) under the F ^α-scheme and discuss the influence of the associated sequence α _n on the limit behaviour of this random variable.     

Asymptotic results for random coefficient bifurcating autoregressive processes

The purpose of this paper is to study the asymptotic behaviour of the weighted least-squares estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and the inheritance, we establish the almost sure convergence of our estimators, as well as a quadratic strong law and central limit theorems. Our study mostly relies on limit theorems for vector-valued martingales.     

Comparison of One-Sided Tolerance Limits in Unbalanced One-Way Random Models

Cox's discrete logistic model was extended to the study of the life table by Thompson (1977) to handle grouped survival data. Inferences about the effect of grouping are studies byMonte Carlo methods. The results show that the effect of grouping is not substantial. This approach is applied to the grouped data on liver cancer. The computer program developed for grouped censored data with continuous and indicator covariates is of practical importance and is available fromThe Ohio State University     

论让步思想让步政策及其作用

在历史发展中,不同的人、阶级、政党、民族、国家都曾使用过不同的让步政策,让步思想经过长时间的演变和发展,出现了各种各样的让步.让步需要有一定的限度,超过限度就达不到让步的目的,甚至走向反面.通过让步,可使让步一方维持自己最起码的“存在”;通过让步,使让步双方共同获得利益;通过让步,使让步双方创造“和平”的时间和空间;通过让步,使让步双方实现共同目标.