We propose a class of weighted least squares estimators for the tail index distribution function with regularly varying tail. Our approach is based on method developed by Holan and McElroy (2010) Parzen index. prove asymptotic normality consistency under suitable assumptions. These earlier are compared in various models through simulation study using mean squared error as criterion. The results...

Tail distribution bounds play a major role in the estimation of failure probabilities in performance and reliability analysis of systems. They are usually estimated using the Markov and Chebyshev’s inequalities, which represent tail distribution bounds for a random variable in terms of its mean or variance. This paper presents the formal verification of Markov’s and Chebyshev’s inequalities for...

Analyzing the future values of anticipated claims is essential in order for insurance companies to avoid major losses caused by prospective claims. This study proposes a novel three-parameter compound Lomax extension. The new density can be "monotonically declining", "symmetric", "bimodal-asymmetric", "asymmetric with right tail", wide peak" or left tail". hazard rate take following shapes: "J-...