Likelihood Confidence Research Articles

Inference for One-Shot Devices with Dependent k-Out-of-M Structured Components under Gamma Frailty

A device that performs its intended function only once is referred to as a one-shot device. Actual lifetimes of such kind of devices under test cannot be observed, and they are either left-censored or right-censored. In addition, one-shot devices often consist of multiple components that could cause the failure of the device. The components are coupled together in the manufacturing process or assembly, resulting in the failure modes possessing latent heterogeneity and dependence. In this paper, we develop an efficient expectation–maximization algorithm for determining the maximum likelihood estimates of model parameters, on the basis of one-shot device test data with multiple failure modes under a constant-stress accelerated life-test, with the dependent components having exponential lifetime distributions under gamma frailty that facilitates an easily understandable interpretation. The maximum likelihood estimate and confidence intervals for the mean lifetime of k-out-of-M structured one-shot device under normal operating conditions are also discussed. The performance of the proposed inferential methods is finally evaluated through Monte Carlo simulations. Three examples including Class-H failure modes data, mice data from ED01 experiment, and simulated data with four failure modes are used to illustrate the proposed inferential methods.

New empirical likelihood inference for the mean residual life with length-biased and right-censored data

ABSTRACT The mean residual life (MRL) function for a given random variable T is the expected remaining lifetime of T after a fixed time point t. It is of great interest in survival analysis, reliability, actuarial applications, duration modelling, etc. Liang, Shen, and He [‘Likelihood Ratio Inference for Mean Residual Life of Length-biased Random Variable’, Acta Mathematicae Applicatae Sinica, English Series, 32, 269–282] proposed empirical likelihood (EL) confidence intervals for the MRL based on length-biased right-censored data. However, their -2log(EL ratio) has a scaled chi-squared distribution. To avoid the estimation of the scale parameter in constructing confidence intervals, we propose a new empirical likelihood (NEL) based on i.i.d. representation of Kaplan–Meier weights involved in the estimating equation. We also develop the adjusted new empirical likelihood (ANEL) to improve the coverage probability for small samples. The performance of the NEL and the ANEL compared to the existing EL is demonstrated via simulations: the NEL-based and ANEL-based confidence intervals have better coverage accuracy than the EL-based confidence intervals. Finally, our methods are illustrated with a real data set.

Working Our Way Out of Privilege: Lessons from South Africa on Preparing White Americans for a National Transitional Justice Process

This study utilized difference-in-differences analysis to determine likelihood of confidence in four major public institutions over three periods of time in South Africa and the United States, two prior to South Africa’s transitional justice process and one after. Results indicate that Black South African confidence rose while White South African confidence dropped drastically. American confidence levels, for both races, remained relatively consistent over all three time periods. The drastic drop in White South African likelihood of confidence points to possible feelings of loss related to power and privilege. These results provide insight for social workers interested in addressing racial injustice in the United States, particularly for White social workers seeking to prepare White individuals for what a transitional justice process may look like and the resulting feelings of loss from the creation of a more equitable state.

Parameter Estimations and Optimal Design of Simple Step-Stress Model for Gamma Dual Weibull Distribution

This paper considers life-testing experiments and how it is effected by stress factors: namely temperature, electricity loads, cycling rate and pressure. A major type of accelerated life tests is a step-stress model that allows the experimenter to increase stress levels more than normal use during the experiment to see the failure items. The test items are assumed to follow Gamma Dual Weibull distribution. Different methods for estimating the parameters are discussed. These include Maximum Likelihood Estimations and Confidence Interval Estimations which is based on asymptotic normality generate narrow intervals to the unknown distribution parameters with high probability. MathCAD (2001) program is used to illustrate the optimal time procedure through numerical examples.

Empirical likelihood inference for the bivariate survival function under univariate censoring

ABSTRACTIn this article, we apply the empirical likelihood method to make inference on the bivariate survival function of paired failure times by estimating the survival function of censored time with the Kaplan–Meier estimator. Adjusted empirical likelihood (AEL) confidence intervals for the bivariate survival function are developed. We conduct a simulation study to compare the proposed AEL method with other methods. The simulation study shows the proposed AEL method has better performance than other existing methods. We illustrate the proposed method by analyzing the skin graft data.

Inferência estatística clássica para a confiabilidade de rede de coautoria com enfoque nos vértices

Um grupo de pesquisa pode ser considerado uma rede social, a qual pode ser modelada por um grafo G composto por k vértices e m arestas. Os pesquisadores que compõem essa rede podem ser interpretados como seus vértices, e as conexões ou ligações entre esses pesquisadores (representadas por trabalhos em coautoria) podem ser consideradas suas arestas. O objetivo deste trabalho foi estudar a medida de confiabilidade de redes considerando os vértices ou pesquisadores não confiáveis e as arestas ou conexões perfeitamente confiáveis. Especificamente, foi proposta uma abordagem inferencial clássica para a confiabilidade de redes, obtendo os estimadores de máxima verossimilhança e os respectivos intervalos de confiança para os componentes individuais (pesquisadores) e para a rede de coautoria; foi aplicada a metodologia a um grupo de pesquisa da UNESP cadastrado no CNPq; e, foram obtidas medidas de centralidade de vértices para auxiliar na identificação de situações onde a inserção de uma aresta ou ligação entre dois pesquisadores do grupo poderia aumentar significativamente a confiabilidade da rede de coautoria. Os resultados mostraram a utilidade da inferência estatística no contexto de confiabilidade de redes sociais, ressaltando que a contribuição de cada pesquisador é de extrema importância para a manutenção de um grupo de pesquisa. Verificou-se ainda que o cálculo da confiabilidade de uma rede de coautoria pode ser bastante desgastante de ser executado e que as medidas de centralidade são uma ferramenta viável quando se intenciona aumentar a confiabilidade dessa rede.

Estimating the number and locations of Euler poles

Plate tectonics is much concerned with Euler poles (axes of rotation) of plates. Each Euler pole has to be estimated from geological field data \(({\mathbf {r}}_1, \pm {\mathbf {n}}_1), \ldots , ({\mathbf {r}}_n,\pm {\mathbf {n}}_n)\), where (for \(i = 1, \ldots , n\)) \({\mathbf {r}}_i\) is a point on the unit sphere, \(S^2\), and \(\pm {\mathbf {n}}_i\) is an axis in the tangent plane at \({\mathbf {r}}_i\). Such data are viewed here as regression data, in which the positions \({\mathbf {r}}_i\) are values of a predictor on \(S^2\), while the corresponding tangential axes \(\pm {\mathbf {n}}_i\) are responses in the tangent plane to \(S^2\) at \({\mathbf {r}}_i\) (\(i = 1, \ldots ,n\)). A regression model is proposed, from which maximum likelihood estimates and confidence regions for the pole can be found. Since samples may come from unknown mixtures of populations, it is necessary to estimate the number of Euler poles and their locations. By extending the above regression model to a mixture model and using the EM algorithm, the number of Euler poles can be estimated and both point estimates and confidence regions for the poles can be obtained. The observations can then be allocated to the estimated Euler poles. The methods are illustrated by the analysis of some artificial data sets.

STUDENTS’ CONFIDENCE IN THEIR FINANCIAL MANAGEMENT ABILITIES: THE ROLE OF SOCIO-DEMOGRAPHIC CHARACTERISTICS AND EDUCATION

The aim of this study was to investigate the impact of gender, age, parent’s education, scholarship and students’ education on students’ confidence in their financial management capability and knowledge. In the research, 259 students participated from two different faculties – the Faculty of Education and the Faculty of Economics. This investigation has revealed that the likelihood of students’ confidence in their financial management capability and knowledge is significantly smaller for students who do not specialize in economics or business studies, and for female students. The likelihood of confidence in their financial management capability and knowledge also statistically significantly increases with the father’s educational level, but, interestingly, not with the mother’s. The results also showed, although it is not statistically significant, that students on scholarships on average express a higher confidence in their financial management capability and knowledge. Therefore, the adequacy of the current educational policy (formal and non-formal education) should be considered. Key words: confidence, education, financial literacy, money management, perception.

Estimation of P(Y

In this article, estimation of the probability Q = P(Y < X) when X and Y are two independent but not identically location-scale distributed random variables under the joint progressively Type-II censoring is studied. The maximum likelihood estimation and confidence intervals using asymptotic distribution and two parametric bootstrap resampling methods for parameter Q are explored. A simulation study concentrating mainly on the extreme-value distribution illustrates the accuracy of these confidence intervals. Finally, a numerical example is used to illustrate the proposed methods.

Stable Distributions for Open Populations Subject to Periodical Reclassifications

Using a Markov model, we study the evolution of open populations subject to periodical reclassifications considering a random number of entrances. In this paper, we focus on the estimation of the subpopulations' relative sizes, obtaining maximum likelihood (ML) estimators, asymptotic distributions, and confidence regions. We show, under general conditions, that the stable distribution is dependent on the rate of entrances to the population. We illustrate the model by estimating the evolution of a population of a pension fund beneficiaries.

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.

On Parameter Inference for Step-Stress Accelerated Life Test with Geometric Distribution

In this article, we present the parameter inference in step-stress accelerated life tests under the tampered failure rate model with geometric distribution. We deal with Type-II censoring scheme involved in experimental data, and provide the maximum likelihood estimate and confidence interval of the parameters of interest. With the help of the Monte-Carlo simulation technique, a comparison of precision of the confidence limits is demonstrated for our method, the Bootstrap method, and the large-sample based procedure. The application of two industrial real datasets shows the proposed method efficiency and feasibility.

Empirical likelihood confidence intervals for regression parameters of the survival rate

The survival probability of patients plays an important role in biomedical settings. Based on the Jung [(1996), ‘Regression Analysis for Long-Term Survival Rate’, Biometrika, 83, 227–232] regression model for survival probability, Zhao [(2005), ‘Regression Analysis for Long-Term Survival Rate Via Empirical Likelihood’, Journal of Nonparametric Statistics, 17, 995–1007] developed an empirical likelihood (EL) confidence region for the vector of regression parameters. However, the proposed EL method does not work for a subset of regression parameters. In this paper, we develop EL confidence regions for any subset or a linear combination of the vectors of the regression parameters under the regression model. We propose two kinds of confidence intervals for the survival rate of a patient with the given covariates. A simulation study is carried out to compare the proposed method with the normal approximation-based method and nonparametric bootstrap method. Finally, we compare the proposed procedure with the existing method using a clinical trial data set.

A microsatellite perspective on the reproductive success of subordinate male honey badgers, Mellivora capensis

The dominance hierarchy system of male honey badg ers, Mellivora capensis, does not appear to determine reproductive success in the species as subordinate males are frequently seen to gain brief access to re ceptive females. To establish whether these interac tions lead to fertilization, five microsatellite loci were used to infer paternity in a honey badger population from the Kgalagadi Transfrontier National Park. In total, 26 individuals comprising 10 cubs, eight known mothers and eight potential fathers were analysed. Exclusion analysis and a likelihood based approach identified the dominant male in the study population as the most likely father of 50% of the cubs (≥80% likelihood confidence). The remaining five cubs were most likely fathered by four different subordi nate males (≥80% likelihood confidence). The results suggest that the brief mating opportunities afforded to subordinate males lead to fertilization, and hence that the dominance hierarchy system of the honey badger is not strong enough to exclude sneak fertil izations.

Confidence intervals for fish out-migration estimates using stratified trap efficiency methods

Marked fish placed above a smolt trap allow fisheries biologists to estimate the efficiency of the trap and hence to estimate the number of smolts migrating past the trap. We compared stratified maximum likelihood estimators and confidence intervals of total numbers of fish migrating to two other well-known estimators and associated confidence intervals using simulation. The Bailey adjusted Lincoln-Petersen estimator and its bootstrap confidence interval performed well overall.

Using exploration history to estimate undiscovered resources

Inference about deposits left to be discovered in a partially explored oil field that require only assumptions about the randomness in the exploration procedure are considered. Unbiased estimators, estimators based on partial likelihood methods and confidence procedures are proposed.

Diagnostics for Assessing the Accuracy of Normal Approximations in Exponential Family Nonlinear Models

Abstract Diagnostics are investigated for assessing the agreement between likelihood and standard large-sample confidence regions for parameters from an exponential family nonlinear model (Cordeiro and Paula 1989). The development connects the contour methods proposed by Hodges (1985, 1987) with the curvature measures for normal, nonlinear regression proposed by Bates and Watts (1980) and Jennings's (1982, 1986) diagnostics for logistic regression. The proposed methodology is illustrated with several examples.

Efficiency of Conditional Maximum Likelihood Estimators and Confidence Limits for Mixtures of Exponential Families

Efficiency of Conditional Maximum Likelihood Estimators and Confidence Limits for Mixtures of Exponential Families

Efficiency of conditional maximum likelihood estimators and confidence limits for mixtures of exponential families

SUMMARY In a previous paper (Basawa, 1981) efficient conditional tests were discussed for mixture experiments involving dependent observations. The present paper is devoted to a study of the performance, in large samples, of a conditional maximum likelihood estimator and of a confidence limit for a parameter in a model specified by a mixture of a two-parameter exponential family. The conditional estimator proposed in the paper is free from the mixing distribution, and is efficient for all reasonable mixing distributions.