In this paper, we extended a repairable system model under general repair that is based on repair history, to incorporate covariates. We calculated the bias, standard error and RMSE of the parameter estimates of this model at different sample sizes using simulated data. We applied the model to a real demonstration data and tested for existence of time trend, repair and covariate effects. Following that we also conducted a coverage probability study on the Wald confidence interval estimates. Finally we conducted hypothesis testing for the parameters of the model.The results indicated that the estimation procedure is working well for the proposed model but the Wald interval should be applied with much caution.
One of the most important lifetime distributions that is used for modelling and analysing data in clinical, life sciences and engineering is the Weibull distribution. The main objective of this paper was to determine the best estimator for the two-parameter Weibull distribution. The methods under consideration are the frequentist maximum likelihood estimator, least square regression estimator and the Bayesian estimator by using two loss functions, which are squared error and linear exponential. Lindley approximation is used to obtain the Bayes estimates. Comparisons are made through simulation study to determine the performance of these methods. Based on the results obtained from this simulation study the Bayesian approach used in estimating the Weibull parameters under linear exponential loss function is found to be superior as compared to the conventional maximum likelihood and least squared methods.
This paper investigates the confidence intervals of R2 MAD, the coefficient of determination based on
median absolute deviation in the presence of outliers. Bootstrap bias-corrected accelerated (BCa)
confidence intervals, known to have higher degree of correctness, are constructed for the mean and standard deviation of R2 MAD for samples generated from contaminated standard logistic distribution. The results indicate that by increasing the sample size and percentage of contaminants in the samples, and perturbing the location and scale of the distribution affect the lengths of the confidence intervals. The results obtained can also be used to verify the bound of R2 MAD.