An improved one-parameter weighted distribution with mathematical properties, estimation, and applications

Abstract

In this study, an improved extension of the Haq distribution was introduced. The new model is named “size-biased Haq distribution (SBHD)”. Its two special cases length-biased and area-biased Haq distribution are discussed. The important mathematical properties such as moments, moment generating function, variance, skewness, kurtosis, Rényi entropy, survival function, hazard function, and mean residual life are derived. The model parameters are estimated using five different estimation methods. A comprehensive simulation study was utilized to illustrate the behavior of derived estimators. Two datasets from different fields are utilized to illustrate the flexibility of the new distributions. It is concluded that the new model is more flexible and efficiently analyzed when the datasets are compared to the considered competitive distributions.

Keywords

• Haq distribution
• Weighted approach
• Moments
• Inference, data analysis