Estimation Parameter of R = P(Y < X) for Length-Biased Weighted Lomax Distributions in the Presence of Outliers

Abstract

The concept of length-biased distribution is applied in expending proper models for lifetime data. The length-biased distribution is a special case of well-known weighted distribution. In this article, we introduce a length-biased weighted Lomax distribution (LBWLD) with k presence of outliers and estimate the parameter of R = P(Y < X) when the random variables X and Y are independent and have LBWLD in presence of outliers and without outliers, respectively. The bias and mean square error (MSE) of the estimator are examined with simulations of numerical and bootstrap resampling. Analysis of a real data set is considered for illustrative purposes.

Keywords

• Lomax distribution
• length-biased weighted Lomax distribution
• outliers
• maximum likelihood estimation
• mean squared error