Abstract
In this article, we introduce a class of distributions that have heavy tails as compared to Pareto distribution of third kind, which we termed as Heavy Tailed Pareto (HP) distribution. Various structural properties of the new distribution are derived. It is shown that HP distribution is in the domain of attraction of minimum of Weibull distribution. A representation of HP distribution in terms of Weibull random variable is obtained. Two characterizations of HP distribution are obtained. The method of maximum likelihood is used for estimation of model parameters and simulation results are presented to assess the performance of new model. Marshall-Olkin Heavy Tailed Pareto (MOHP) distribution is also introduced and some of its properties are studied. It is shown that MOHP distribution is geometric extreme stable. An autoregressive time series model with the new model as marginal distribution is developed and its properties are studied.
Highlights
Data with heavy tails have been studied by various researchers in different areas such as economics, finance, reliability, telecommunications, high speed network traffic, hydrology, insurance, linguistics, physics, biology, etc
We refer this distribution as Marshall-Olkin Heavy Tailed Pareto distribution, denoted by MOHP(α, λ)
The maximum likelihood estimates of the parameters α and λ of MOHP distribution are obtained by solving the equations, n λ
Summary
Data with heavy tails have been studied by various researchers in different areas such as economics, finance, reliability, telecommunications, high speed network traffic, hydrology, insurance, linguistics, physics, biology, etc. Various forms of the Pareto distribution have been formulated for modelling and analysis of data from engineering, environment, geology, hydrology, actuarial science, telecommunications, reliability, risk modelling, etc. These diverse applications of Pareto distribution lead researchers to develop different generalizations of Pareto distribution. Despite the importance of Pareto distribution in data modelling, a comprehensive study on distributions heavier than Pareto distribution in the context of heavy-tailed distributions has not been considered so far Motivated by this fact, we introduce here, a new distribution whose tail is heavier than that of Pareto distribution.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
