Predicting Failure times for some Unobserved Events with Application to Real-Life Data

This study aims to predict failure times for some units in some lifetime experiments. In some practical situations, the experimenter may not be able to register the failure times of all units during the experiment. Recently, this situation can be described by a new type of censored data called multiply-hybrid censored data. In this paper, the linear failure rate distribution is well-fitted to some real-life data and hence some statistical inference approaches are applied to estimate the distribution parameters. A two-sample prediction approach applied to extrapolate a new sample simulates the observed data for predicting the failure times for the unobserved units

Parameter Estimation and Prediction of Future Failures in the Log-Logistic Distributions Based on Hybrid-Censored Data

The main purpose of this thesis is to study the prediction of future observations of a Log-Logistic distribution from Hybrid Censored Samples. We will study parameter point estimation, interval estimation, different point predictors will be formed such as Maximum Likelihood Predictor (MLP), Best Unbiased Predictor (BUP), and Conditional Median Predictor (CMP). Different Prediction intervals will be constructed such as Intervals based on Pivotal quantities, and High-Density Intervals (HDI). A simulation study will be run using the R software to investigate and compare the performance of all point predictors and prediction intervals. It is observed that the (BUP) is the best point predictor and the (HDI) is the best prediction interval

A missing composite covariate in survival analysis: a case study of the Chinese Longitudinal Health and Longevity Survey

We estimate a Cox proportional hazards model where one of the covariates measures the level of a subject´s cognitive functioning by grading the total score obtained by the subject on the items of a questionnaire. A case study is presented where the sample includes partial respondents, who did not answer some or all of the questionnaire items. The total score takes hence the form of an interval-censored variable and, as a result, the level of cognitive functioning is missing on some subjects. We handle partial respondents by taking a likelihood-based approach where survival time is jointly modelled with the censored total score and the size of the censoring interval. Parameter estimates are obtained by an E-M-type algorithm that essentially reduces to the iterative maximization of three complete log-likelihood functions derived from two augmented datasets with case weights, alternated with weights updating. This methodology is exploited to assess the Mini Mental State Examination index as a prognostic factor of survival in a sample of Chinese older adults.China, health

Hierarchical Bayes Estimation of Reliability Indexes of Cold Standby Series System under General Progressive Type II Censoring Scheme

In this paper, hierarchical Bayes approach is presented for estimation and prediction of reliability indexes and remaining lifetimes of a cold standby series system under general progressive Type II censoring scheme. A simulation study has been carried out for comparison purpose. The study will help reliability engineers in various industrial series system setups

A new least squares method for estimation and prediction based on the cumulative Hazard function

In this paper, the cumulative hazard function is used to solve estimation and prediction problems for generalized ordered statistics (defined in a general setup) based on any continuous distribution. The suggested method makes use of Rényi representation. The method can be used with type Ⅱ right-censored data as well as complete data. Extensive simulation experiments are implemented to assess the efficiency of the proposed procedures. Some comparisons with the maximum likelihood (ML) and ordinary weighted least squares (WLS) methods are performed. The comparisons are based on both the root mean squared error (RMSE) and Pitman's measure of closeness (PMC). Finally, two real data sets are considered to investigate the applicability of the presented methods

On Progressively Type-II Censored Two-Parameter Rayleigh Distribution

Abstract Recently, Rayleigh distribution has received considerable attention in the statistical literature. In this paper, we consider the point and interval estimation of the functions of the unknown parameters of a two-parameter Rayleigh distribution. First, we obtain the maximum likelihood estimators (MLEs) of the unknown parameters. The MLEs cannot be obtained in explicit forms, and we propose to use the maximization of the profile log-likelihood function to compute the MLEs. We further consider the Bayesian inference of the unknown parameters. The Bayes estimates and the associated credible intervals cannot be obtained in closed forms. We use the importance sampling technique to approximate (compute) the Bayes estimates and the associated credible intervals. For comparison purposes we have also used the exact method to compute the Bayes estimates and the corresponding credible intervals. Monte Carlo simulations are performed to compare the performances of the proposed method, and one data set has been analyzed for illustrative purposes. We further consider the Bayes prediction problem based on the observed samples, and provide the appropriate predictive intervals. A data example has been provided for illustrative purposes

Statistical analysis of Gompertz distribution based on progressively type-II censored competing risk model with binomial removals

Here in this paper, we consider the progressive Type-II censoring Gompertz data under competing risks model with binomial removals. The maximum likelihood estimators of the model parameters involved are obtained by applying numerical methods and the asymptotic variance-covariance matrix of the estimators is also derived. Bayesian estimates based on importance sampling procedure are developed under squared error, LINEX and general entropy loss functions. The confidence intervals using the asymptotic normality and Bayesian approaches are also developed. Finally, a Monte Carlo simulation is conducted to evaluate the performance of the so proposed estimators under all these different estimation methods

Statistical analysis of Gompertz distribution based on progressively type-II censored competing risk model with binomial removals

Here in this paper, we consider the progressive Type-II censoring Gompertz data under competing risks model with binomial removals. The maximum likelihood estimators of the model parameters involved are obtained by applying numerical methods and the asymptotic variance-covariance matrix of the estimators is also derived. Bayesian estimates based on importance sampling procedure are developed under squared error, LINEX and general entropy loss functions. The confidence intervals using the asymptotic normality and Bayesian approaches are also developed. Finally, a Monte Carlo simulation is conducted to evaluate the performance of the so proposed estimators under all these different estimation methods