Optimal B-robust estimators for the parameters of the Burr XII distribution

Abstract

The Burr XII distribution offers a flexible alternative to the distributions that play important role for modelling data in reliability, risk and process capability. However, estimating the shape parameters of the Burr XII distribution is a challenging problem. The classical estimation methods such as maximum likelihood and least squares are often used to estimate the parameters of the Burr XII distribution, but these methods are very sensitive to the outliers in the data. Thus, a robust estimation method alternative to the classical methods is needed to find robust estimators that are less sensitive to the outliers in the data. The purpose of this paper is to use the optimal B-robust estimation method [Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA. Robust statistics: the approach based on influence functions. New York: Wiley; 1986] to obtain robust estimators for the shape parameters of the Burr XII distribution. The simulation results show that the optimal B-robust estimators generally outperform the classical estimators in terms of the bias and root mean square errors when there are outliers in data.

On Modified Log Burr XII Distribution

“…Thupeng (2016) modeled concentrations of the daily extreme nitrogen dioxide with BXII distributions. Doǵru and Arslan (2016) estimated the parameters of BXII distributions with optimal B-robust estimators. Yari and Tondpour (2017) derived a new Burr distribution to study the lifetime cancer data.…”

Robust parameter estimation for the Marshall-Olkin extended Burr XII distribution

“…In this section we will discuss the least squares method for estimating ; c and k. As for the Burr XII distribution [4], LS estimation method can be used as an alternative to the ML estimation method to estimate the parameters of the MOEBXII distribution. The LS method is a combination of parametric (F ) and non-parametric b F distribution functions.…”

“…Failure Time Data Set. Failure time data set has been considered by [4] to illustrate the performance of the proposed robust estimators for the parameters of the Burr XII distribution and by [5] to illustrate the proposed Optimal B-robust estimators for the parameters of the Burr XII distribution. The data set has been also used by [20] to illustrate the potential of the Burr XII power series distributions.…”

“…The minimum variance linear unbiased estimators (MVLUE), the best linear invariant estimators (BLIE) and the maximum likelihood estimators (MLE) based on n-selected generalized order statistics are presented for the parameters of the Burr XII distribution by [13]. An alternative robust estimation methods based on M estimators and optimal B-robust estimation method for the parameters of Burr XII distribution have been proposed by [4] and [5], respectively. However, there is not much work for MOEBXII distribution.…”

Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution

“…To deal with outliers in data M estimation method can be used to obtain robust estimators for the parameters of Burr XII[6] and MOEBXII distribution. The M estimation method estimate the parameters of interest by minimizing the following objective function with the Huber or Tukey function[17].…”