Bayesian estimation for Poisson process models with grouped data and covariate

This paper looks into the Bayesian approach for analyzing and selecting the best Poisson process model for grouped failure data from a repairable system with covariate. The extended powerlaw model with a recurrence rate that incorporates both time and covariate effect is compared to the powerlaw, log-linear and HPP models. We propose the use of both informative and noninformative priors depending on the nature of the parameter. The MCMC technique is utilized to obtain samples from the posterior distribution which was implemented via WinBUGS. We then apply the Bayesian Deviance Information Criteria (DIC) to select the best model for real data from ball bearing failures where information regarding previous failures are available. The credible interval is used to check the significance of the parameters of the selected model. We also used the posterior predictive distribution for model checking by comparing the observed and posterior predictive mean number of failures

Jackknife and bootstrap inferential procedures for censored survival data

Confidence interval is an estimate of a certain parameter. Classical construction of confidence interval based on asymptotic normality (Wald) often produces misleading inferences when dealing with censored data especially in small samples. Alternative techniques allow us to construct the confidence interval estimation without relying on this assumption. In this paper, we compare the performances of the jackknife and several bootstraps confidence interval estimates for the parameters of a log logistic model with censored data and covariate. We investigate their performances at two nominal error probability levels and several levels of censoring proportion. Conclusions were then drawn based on the results of the coverage probability study

Inferential procedures based on the double bootstrap for log logistic regression model with censored data

Traditional inferential procedures based on the asymptotic normality assumption such as the Wald often produce misleading inferences when dealing with censored data and small samples. Alternative estimation techniques such as the jackknife and bootstrap percentile allow us to construct the interval estimates without relying on any classical assumptions. Recently, the double bootstrap became preferable as it is not only free from any classical assumptions, but also has higher order of accuracy. In this paper, we compare the performances of the interval estimates based on the double bootstrap without pivot with the Wald, jackknife and bootstrap percentile interval estimates for the parameters of the log logistic model with right censored data and covariates via a coverage probability study. Based on the results of the study, we concluded that the double bootstrap without pivot technique works better than the other interval estimation techniques, even when sample size is 25. The double bootstrap without pivot technique worked well with real data on hypernephroma patients

The Gompertz flexible Weibull distribution and its applications

This paper introduces the Gompertz flexible Weibull distribution as an extension of the flexible Weibull distribution. Its various statistical properties are obtained and established while the method of maximum likelihood estimation is used in estimating the unknown model parameters. The application of Gompertz flexible Weibull distribution is illustrated by making use of three real life data sets, this is done to demonstrate its potentials over some other important distributions like the Gompertz Weibull, Gompertz Burr type XII, Gompertz Lomax, exponentiated flexible Weibull, exponentiated flexible Weibull extension and Kumaraswamy flexible Weibull distributions. Simulation studies were also conducted and the behavior of the Gompertz flexible Weibull parameters were investigated

A parametric model for doubly interval censored lifetime

Doubly interval censored data is defined as elapsed time between two related events that is subject to interval or right censoring. In this paper, we extended a parametric model to incorporates doubly interval-, interval-, right censored and uncensored lifetime data. We assumed the initial event time follows uniform distribution and the lifetime follows the log logistic distribution. The interval censored event times are imputed using midpoint of their intervals for ease of the estimation process. The estimation procedure is studied at different sample sizes and attendance probabilities using simulated data. Finally, we study the Wald method of constructing confidence interval estimates for the parameters of the model. Conclusions were drawn based on the coverage probability study

Inferential procedures for log logistic distribution with doubly interval censored data

The log logistic model with doubly interval censored data is examined. Three methods of constructing confidence interval estimates for the parameter of the model were compared and discussed. The results of the coverage probability study indicated that the Wald outperformed the likelihood ratio and jackknife inferential procedures

Exponentiated Weibull Burr Type X Distribution’s Properties and Its Applications

This study proposes a new distribution called exponentiated Weibull Burr type X distribution which provides greater flexibility in fitting the survival data. We derive several statistical properties of the proposed distribution, which consist of the quantile function, moment, order statistics, and Renyi entropy. We use maximum likelihood approach to estimate the proposed distribution’s parameters. Simulation study is then conducted with varying samples sizes and parameter values for examining the performance of the suggested distribution. Lastly, real data are used to illustrate the flexibility and performance of the proposed distribution, its sub-models, and some extension of Burr type X distribution. The results reveal that the suggested distribution yields a better model fit in comparison with other competing models. In conclusion, the proposed distribution able to model a wide range of survival data, including data with decreasing, increasing, bathtub, and unimodal hazard functions. Perhaps it may perform better than its sub-models in fitting the survival data

Exponentiated Weibull Burr Type X Distribution’s Properties and Its Applications

This study proposes a new distribution called exponentiated Weibull Burr type X distribution which provides greater flexibility in fitting the survival data. We derive several statistical properties of the proposed distribution, which consist of the quantile function, moment, order statistics, and Renyi entropy. We use maximum likelihood approach to estimate the proposed distribution’s parameters. Simulation study is then conducted with varying samples sizes and parameter values for examining the performance of the suggested distribution. Lastly, real data are used to illustrate the flexibility and performance of the proposed distribution, its sub-models, and some extension of Burr type X distribution. The results reveal that the suggested distribution yields a better model fit in comparison with other competing models. In conclusion, the proposed distribution able to model a wide range of survival data, including data with decreasing, increasing, bathtub, and unimodal hazard functions. Perhaps it may perform better than its sub-models in fitting the survival data

A new exponentiated beta burr type X distribution : model, theory, and applications

In recent years, many attempts have been carried out to develop the Burr type X distribution, which is widely used in fitting lifetime data. These extended Burr type X distributions can model the hazard function in decreasing, increasing and bathtub shapes, except for unimodal. Hence, this paper aims to introduce a new continuous distribution, namely exponentiated beta Burr type X distribution, which provides greater flexibility in order to overcome the deficiency of the existing extended Burr type X distributions. We first present its density and cumulative function expressions. It is then followed by the mathematical properties of this new distribution, which include its limit behaviour, quantile function, moment, moment generating function, and order statistics. We use maximum likelihood approach to estimate the parameters and their performance is assessed via a simulation study with varying parameter values and sample sizes. Lastly, we use two real data sets to illustrate the performance and flexibility of the proposed distribution. The results show that the proposed distribution gives better fits in modelling lifetime data compared to its sub-models and some extended Burr type X distributions. Besides, it is very competitive and can be used as an alternative model to some nonnested models. In summary, the proposed distribution is very flexible and able to model various shaped hazard functions, including the increasing, decreasing, bathtub, and unimodal