Minimum variance unbiased estimation of stress–strength reliability under bivariate normal and its comparisons

In many industrial and natural phenomena, we need the probability that a component is smaller than the other component. Under a stress–strength model, this is reliability of an item. Under independent setup, there are different approaches for the estimation of such reliability. Here, estimation is considered under the dependent case. Under bi-variate setup uniformly minimum variance unbiased estimator is obtained. Also comparison with available estimator based on Maximum Likelihood Estimate (MLE) is done through Mean Square Error (MSE) and bias. Also these are compared by computing L₁ distance between their distribution functions. From this idea and numerical computations, UMVUE appears to be good.     

The Frisch–Waugh–Lovell theorem for the lasso and the ridge regression

The Frisch–Waugh–Lovell (FWL) (partitioned regression) theorem is essential in regression analysis. This is partly because it is quite useful to derive theoretical results. The lasso regression and the ridge regression, both of which are penalized least-squares regressions, have become popular statistical techniques. This article describes that the FWL theorem remains valid for these penalized least-squares regressions. More precisely, we demonstrate that the covariates corresponding to unpenalized regression parameters in these penalized least-squares regression can be projected out. Some other results related to the FWL theorem in such penalized least-squares regressions are also presented.     

我国排污权交易制度的应用研究

排污权交易制度作为一种新的治理企业污染的市场手段比政府行政管制手段具有更大的优势,它将市场机制充分地运用于环境资源的配置,在总量控制的前提下,通过排污权的交易,实现低成本治理污染,有利于环境保护和经济的可持续发展.我国已经具有了实施排污权交易的基本条件,根据我国的现实国情,设计了包括立法、信息公示、监控系统、总量控制、排污权的初始分配和市场交易等六部分构成的排污权交易制度,提出了我国实现排污权交易一些急待解决的问题.     

关于Feigenbaum型泛函方程的C^1解

利用Schauder不动点定理、自同胚和紧凸子集的相关性质研究Feigenbaum型泛函方程的连续可微解的存在性和唯一性.     

A probabilistic approach to Wallis’ formula

We present an alternative proof of Wallis’ formula from the probabilistic point of view. Based on the classical central limit theorem, some discrete distributions with additive property, such as binomial, negative binomial, Poisson and multinomial distributions, are considered to derive π/2.     

A simple approximation for the doubly noncentral t-distribution

A simple approximation for the doubly noncentral t-distribution, based upon the Fieller-Geary Theorem (1930) and approximate normality of the square root of the noncentral chi-square variable observed by Patnaik (1949), is developed, This approximation and an Edgeworth series expansion associated with it are evaluated. The simple approximation is seen to be reasonably accurate for most practical purposes.     

A process capability index with reliable confidence intervals

A well-know process capability index is slightly modified in this article to provide a new measure of process capability which takes account of the process location and variability, and for which point estimator and confidence intervals do exist that are insensitive to departures from the assumption of normal variability. Two examples of applications based on real data are presented.     

Proportional Trapping-Removal Model with a Known Ratio

ABSTRACT

Population size estimator is derived for a proportional trapping-removal model with a known ratio between two sub-population sizes, and the corresponding asymptotic properties is obtained. The performance of the proposed estimator is checked via simulation studies and an example.