The estimation of the Burr-XII parameters with middle-censored data

Abstract

Middle-censoring is considered as a modern general scheme of censoring. In this paper, we study the analysis of middle-censored data with Burr-XII distribution which is considered one of the most popular and flexible distributions for modeling stochastic events and lifetime for many products.The parameters are estimated by the maximum likelihood method and the Bayes estimation under gamma prior and by applying the Lindley’s approximation.A simulation study is carried out to compare the performances of the two estimates. Both estimators behave almost similarly and verified the consistency property. A real medical data set is considered for illustration.

Estimation of the location and the scale parameters of Burr Type XII distribution

“…It is clear that the likelihood equations cannot be solved explicitly because of the non-linear functions g 1 (z i ) and g 2 (z i ) in 3and (4). Therefore, we resort to iterative methods for solving them.…”

“…Dogru and Arslan [14] obtained the optimal B-robust estimators for the shape parameters of the Burr Type XII distribution. In addition to these studies, inference for the Burr Type XII distribution has been considered under di¤erent scenarios such as type-II censored data [41], progressively censored data [29], multiple censored data [38], record data [21], progressive …rst-failure censored data [30] and middlecensored data [4]. Furthermore, many authors are interested in the generalized version of Burr Type XII distribution in recent years.…”

New Modified Burr III Distribution, Properties and Applications

“…Then, the exact value of is observable only if , otherwise the interval is observed. Middle-censoring has been applied to exponential and Burr-XII lifetime distributions [18,20]. Furthermore, it was extended to parametric models with covariates, [21] and then its robustness was investigated by [22].…”