Inference under progressively type II right censored sampling for certain lifetime distributions

In this paper, estimation of the parameters of a certain family of two-parameter lifetime distributions based on progressively Type II right censored samples (including ordinary Type II right censoring) is studied. This family, of reverse hazard distributions, includes the Weibull, Gompertz and Lomax distributions. A new type of parameter estimation, named inverse estimation, is introduced for both parameters. Exact confidence intervals for one of the parameters and generalized confidence intervals for the other are explored; inference for the first parameter can be accomplished by our methodology independently of the unknown value of the other parameter in this family of distributions. Derivation of the estimation method uses properties of order statistics. A simulation study in the particular context of the Weibull distribution illustrates the accuracy of these confidence intervals and compares inverse estimators favorably with maximum likelihood estimators. A numerical example is used to illustrate the proposed procedures

Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions

Accelerated life tests are used to explore the lifetime of extremely reliable items by subjecting them to elevated stress levels from stressors to cause early failures, such as temperature, voltage, pressure, and so on. The alpha power inverse Weibull (APIW) distribution is of great significance and practical applications due to its appealing characteristics, such as its flexibilities in the probability density function and the hazard rate function. We analyze the step stress partially accelerated life testing model with samples from the APIW distribution under adaptive type II progressively hybrid censoring. We first obtain the maximum likelihood estimates and two types of approximate confidence intervals of the distributional parameters and then derive Bayes estimates of the unknownparameters under different loss functions. Furthermore, we analyze three probable optimum test techniques for identifying the best censoring under different optimality criteria methods. We conduct simulation studies to assess the finite sample performance of the proposed methodology. Finally, we provide a real data example to further demonstrate the proposed technique

Bayesian Estimation of the Parameters of Two-Component Mixture of Rayleigh Distribution under Doubly Censoring

Recently, the Bayesian analysis of the two-component mixture of lifetime models under singly type I censored samples was discussed. The Bayes estimation of the parameters of mixture of two Rayleigh distributions (MTRD) is developed under doubly censoring. Different informative priors, under squared error loss function and k-loss function, have been assumed for the posterior estimation. The performance of different estimators has been compared in terms of posterior risks by analyzing the simulated and real life data sets

EM algorithm for mixture distributions model with type-I hybrid censoring scheme

[[abstract]]An expectation–maximization (EM) likelihood estimation procedure is proposed to obtain the maximum likelihood estimates of the parameters in a mixture distributions model based on type-I hybrid censored samples when the mixture proportions are unknown. Three bootstrap methods are applied to construct the confidence intervals of the model parameters. Monte Carlo simulations are conducted to evaluate the performance of the proposed methods. Simulation results show that the proposed methods can perform well to obtain reliable point and interval estimation results. Three examples are used to illustrate the applications of the proposed methods.[[notice]]補正完

Order-statistics-based inferences for censored lifetime data and financial risk analysis

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis focuses on applying order-statistics-based inferences on lifetime analysis and financial risk measurement. The first problem is raised from fitting the Weibull distribution to progressively censored and accelerated life-test data. A new orderstatistics- based inference is proposed for both parameter and con dence interval estimation. The second problem can be summarised as adopting the inference used in the first problem for fitting the generalised Pareto distribution, especially when sample size is small. With some modifications, the proposed inference is compared with classical methods and several relatively new methods emerged from recent literature. The third problem studies a distribution free approach for forecasting financial volatility, which is essentially the standard deviation of financial returns. Classical models of this approach use the interval between two symmetric extreme quantiles of the return distribution as a proxy of volatility. Two new models are proposed, which use intervals of expected shortfalls and expectiles, instead of interval of quantiles. Different models are compared with empirical stock indices data. Finally, attentions are drawn towards the heteroskedasticity quantile regression. The proposed joint modelling approach, which makes use of the parametric link between the quantile regression and the asymmetric Laplace distribution, can provide estimations of the regression quantile and of the log linear heteroskedastic scale simultaneously. Furthermore, the use of the expectation of the check function as a measure of quantile deviation is discussed

Estimations and optimal censoring schemes for the unified progressive hybrid gamma-mixed Rayleigh distribution

Censoring is a common occurrence in reliability engineering tests. This article considers estimation of the model parameters and the reliability characteristics of the gamma-mixed Rayleigh distribution based on a novel unified progressive hybrid censoring scheme (UPrgHyCS), where experimenters are allowed more flexibility in designing the test and higher efficiency. The maximum likelihood estimates of the model parameters and reliability are provided using the stochastic expectation–maximization algorithm based on the UPrgHyCS. Further, the Bayesian inference associated with any parametric function of the model parameters is considered using the Markov chain Monte Carlo method with the Metropolis-Hastings (M-H) algorithm. Asymptotic confidence and credible intervals of the proposed quantities are also created. The maximum a posteriori estimates of the model parameters are acquired. Due to the importance of determining the optimal censoring scheme for reliability problems, different optimality criteria are proposed and derived to find it. This method can help to design experiments and get more information about unknown parameters for a given sample size. Finally, comprehensive simulation experiments are provided to investigate the performances of the considered estimates, and a real dataset is analyzed to elucidate the practical application and the optimality criterion work in real life scenarios. The Bayes estimates using the M-H technique show the best performance in terms of error value

Modified weibull distributions in reliability engineering

Ph.DDOCTOR OF PHILOSOPH