Bayesian estimation for Dagum distribution based on progressive type I interval censoring

In this paper, we consider Dagum distribution which is capable of modeling various shapes of failure rates and aging criteria. Based on progressively type-I interval censoring data, we first obtain the maximum likelihood estimators and the approximate confidence intervals of the unknown parameters of the Dagum distribution. Next, we obtain the Bayes estimators of the parameters of Dagum distribution under the squared error loss (SEL) and balanced squared error loss (BSEL) functions using independent informative gamma and non informative uniform priors for both scale and two shape parameters. A Monte Carlo simulation study is performed to assess the performance of the proposed Bayes estimators with the maximum likelihood estimators. We also compute credible intervals and symmetric 100(1 − τ)% two-sided Bayes probability intervals under the respective approaches. Besides, based on observed samples, Bayes predictive estimates and intervals are obtained using one-and two-sample schemes. Simulation results reveal that the Bayes estimates based on SEL and BSEL performs better than maximum likelihood estimates in terms of bias and MSEs. Besides, credible intervals have smaller interval lengths than confidence interval. Further, predictive estimates based on SEL with informative prior performs better than non-informative prior for both one and two sample schemes. Further, the optimal censoring scheme has been suggested using a optimality criteria. Finally, we analyze a data set to illustrate the results derived.

Survival Analysis in The Presence of a Cure Fraction Using Data of Dialysis Patients: A Bayesian Approach

Background: The aim of this study was to evaluate the goodness of fit of Bayesian mixture and non-mixture cure models to find the factors affecting dialysis patient’s survival time where a significant proportion of the population has a long-term survival.Study Design: A retrospective cohort study. Methods: The data of 252 dialysis patients were used among whom 35 cases died. Since in this study a part of the population had long-term survival, Bayesian cure models were used and evaluated using DIC index. The data were analyzed by R and Openbugs Softwares. Results: Of the 252 dialysis patients, 136(54%) were males and the mean (SD) age was 53.39 (18.09) years. The patient’s follow-up time mean (SD) was 10.93(7.82) years. The 10 and 20-year survival rate of these patients were 87% and 73%, respectively. The findings show that the best fitting belonged to the Bayesian Non-mixture Cure Model (BNCM) with Dagum distribution. The variables of age, Body Mass Index, dialysis duration, frequency of dialysis, age of onset of dialysis, and occupation affected patients' survival based on BNCM with Dagum distribution.Conclusions: The results demonstrated that the BNCM with Dagum distribution can be a good selection model to analyze survival data, where there is the possibility of a fraction of cure.

The Zubair-dagum Distribution

This article examines the flexibility of the Zubair-G family of distribution using the Dagum distribution. The proposed distribution is called the Zubair-Dagum distribution. The various mathematical properties of this distribution such as the Quantile function, Moments, Moment generating function, Reliability analysis, Entropy and Order statistics were obtained. The parameter estimates of the proposed distribution were also derived and estimated using the maximum likelihood estimation method. The new distribution is right skewed and has various bathtub and monotonically decreasing shapes. Our numerical illustrations using two real-life datasets substantiate the applicability, flexibility and superiority of the proposed distribution over competing distributions.