Heavy-tailed exponential distribution: Basic properties and parameter estimation

Heavy-tailed exponential distribution is a direct and necessary extension of the heavy-tailed Rayleigh distribution. First, some basic properties of heavy-tailed exponential distribution are introduced in this paper including the series form of the density function, the heavy-tailed property and the non-existence of finite variance. Second, ratio estimator, logarithmic moment estimator and iterative logarithmic moment estimator are presented to estimate the parameters of heavy-tailed exponential distribution based on negative-order moments. The logarithmic moment estimator with explicit closed form is only determined by samples, and the iterative logarithmic moment estimator achieves better performance only using fewer samples in each step computation. Monte Carlo simulation results demonstrate the high efficiency of the iterative logarithmic moment estimator for heavy-tailed exponential distribution.