Goodness-of-fit test for exponentiality based on spacings for general progressive Type-II censored data

There have been numerous tests proposed to determine whether or not the exponential model is suitable for a given data set. In this article, we propose a new test statistic based on spacings to test whether the general progressive Type-II censored samples are from exponential distribution. The null distribution of the test statistic is discussed and it could be approximated by the standard normal distribution. Meanwhile, we propose an approximate method for calculating the expectation and variance of samples under null hypothesis and corresponding power function is also given. Then, a simulation study is conducted. We calculate the approximation of the power based on normality and compare the results with those obtained by Monte Carlo simulation under different alternatives with distinct types of hazard function. Results of simulation study disclose that the power properties of this statistic by using Monte Carlo simulation are better for the alternatives with monotone increasing hazard function, and otherwise, normal approximation simulation results are relatively better. Finally, two illustrative examples are presented.     

Bayes Inference in Constant Partially Accelerated Life Tests for the Generalized Exponential Distribution with Progressive Censoring

In this paper, the problem of constant partially accelerated life tests when the lifetime follows the generalized exponential distribution is considered. Based on progressive type-II censoring scheme, the maximum likelihood and Bayes methods of estimation are used for estimating the distribution parameters and acceleration factor. A Monte Carlo simulation study is carried out to examine the performance of the obtained estimates.     

Accuracy of approximate progressively censored reliability sampling plans for exponential models

Reliability sampling plans provide an efficient method to determine the acceptability of a product based upon the lifelengths of some test units. Usually, they depend on the producer and consumer’s quality requirements and do not admit closed form solutions. Acceptance sampling plans for one- and two-parameter exponential lifetime models, derived by approximating the operating characteristic curve, are presented in this paper. The accuracy of these approximate plans, which are explicitly expressible and valid for failure and progressive censoring, is assessed. The approximation proposed in the one-parameter case is found to be practically exact. Explicit lower and upper bounds on the smallest sample size are given in the two-parameter case. Some additional advantages are also pointed out.     

An additive subdistribution hazard model for competing risks data

The cumulative incidence function plays an important role in assessing its treatment and covariate effects with competing risks data. In this article, we consider an additive hazard model allowing the time-varying covariate effects for the subdistribution and propose the weighted estimating equation under the covariate-dependent censoring by fitting the Cox-type hazard model for the censoring distribution. When there exists some association between the censoring time and the covariates, the proposed coefficients’ estimations are unbiased and the large-sample properties are established. The finite-sample properties of the proposed estimators are examined in the simulation study. The proposed Cox-weighted method is applied to a competing risks dataset from a Hodgkin's disease study.     

Exact confidence bounds for an exponential parameter under hybrid censoring

Consider a life testing experiment in which n units are put on test, successive failure times are recorded, and the observation is terminated either at a specified number r of failures or a specified time T whichever is reached first. This mixture of type I and type II censoring schemes, called hybrid censoring, is of wide use. Under this censoring scheme and the assumption of an exponential life distribution, the distribution of the maximum likelihood estimator of the mean life 6 is derived. It is then used to construct an exact lower confidence bound for θ.     

Judging childhood

This article brings ethnohistorical inquiry to bear in exploring the certainties of Progressive Era reformers regarding the role of the state, the meaning of childhood, and the power of intervention in the lives of children, youth, and families in Butte, Montana. The author draws on the key themes of the Just Practice perspective (Finn & Jacobson, 2008)—as an organizing frame to explore assumptions and contestations regarding childhood, well-being, trouble, and intervention as expressed through primary source documents and reports of juvenile court proceedings in Butte from 1900 to 1914. Butte, a site of rapid industrialization at the turn of the last century, provides a local context in which to examine ways these certainties were asserted, negotiated, embedded, and resisted in the making of a nascent system of child welfare and juvenile justice. The historical analysis offers a foundation for critical reflection on the certainties embedded in contemporary practice with children and youth.     

On the simple step-stress model for two-parameter exponential distribution

In this paper, we consider the simple step-stress model for a two-parameter exponential distribution, when both the parameters are unknown and the data are Type-II censored. It is assumed that under two different stress levels, the scale parameter only changes but the location parameter remains unchanged. It is observed that the maximum likelihood estimators do not always exist. We obtain the maximum likelihood estimates of the unknown parameters whenever they exist. We provide the exact conditional distributions of the maximum likelihood estimators of the scale parameters. Since the construction of the exact confidence intervals is very difficult from the conditional distributions, we propose to use the observed Fisher Information matrix for this purpose. We have suggested to use the bootstrap method for constructing confidence intervals. Bayes estimates and associated credible intervals are obtained using the importance sampling technique. Extensive simulations are performed to compare the performances of the different confidence and credible intervals in terms of their coverage percentages and average lengths. The performances of the bootstrap confidence intervals are quite satisfactory even for small sample sizes.     

Exact likelihood inference for Laplace distribution based on Type-II censored samples

We develop exact inference for the location and scale parameters of the Laplace (double exponential) distribution based on their maximum likelihood estimators from a Type-II censored sample. Based on some pivotal quantities, exact confidence intervals and tests of hypotheses are constructed. Upon conditioning first on the number of observations that are below the population median, exact distributions of the pivotal quantities are expressed as mixtures of linear combinations and of ratios of linear combinations of standard exponential random variables, which facilitates the computation of quantiles of these pivotal quantities. Tables of quantiles are presented for the complete sample case.     

Inference for the scale parameter of lifetime distribution of k-unit parallel system based on progressively censored data

In this paper, inference for the scale parameter of lifetime distribution of a k-unit parallel system is provided. Lifetime distribution of each unit of the system is assumed to be a member of a scale family of distributions. Maximum likelihood estimator (MLE) and confidence intervals for the scale parameter based on progressively Type-II censored sample are obtained. A β-expectation tolerance interval for the lifetime of the system is obtained. As a member of the scale family, half-logistic distribution is considered and the performance of the MLE, confidence intervals and tolerance intervals are studied using simulation.     

Dependence Estimation Over a Finite Bivariate Failure Time Region

This articleconcerns nonparametric estimation of association between bivariatefailure times. In the presence of independent right censoring,the support for failure time variates may be restricted and measuresof dependence over a finite failure time region may be of particularinterest. To this end, the reciprocal cross ratio function, weightedby the bivariate failure time density, is proposed as a summarymeasure of dependence over a failure time region. This `relativerisk' estimator is shown to be consistent and asymptoticallynormally distributed, with consistent bootstrap variance estimator.A finite-region version of Kendall's tau, which is suitable forcensored failure time data, is also proposed, and correspondingasymptotic distribution theory is noted. The accuracy of theseasymptotic approximations is studied in simulations and an illustrationis provided.