Parameter Estimation for the Double Pareto Distribution
Faris M. Al-Athari
DOI : 10.3844/jmssp.2011.289.294
Journal of Mathematics and Statistics
Volume 7, Issue 4
Problem statement: The double Pareto distribution appeared most often as model for variety of fields, including archaeology, biology, economics, environmental science, finance and physics. The distribution exhibits Paretian power-law behavior in both tails. The family of double Pareto distributions has recently been proposed for modeling growth rates such as annual gross domestic product, stock prices, foreign currency exchange rates and company sizes. In this study, I develop parameter estimates for the double Pareto distribution that are easy to compute. I compare the performance of the maximum likelihood estimate with Bayesian and the method of moments estimates. Approach: This study contracted with maximum likelihood, the method of moments and Bayesian using Jeffrey’s prior and the extension of Jeffrey’s prior information. The comparisons are made on the performance of these estimators with respect to the Mean Squared Error (MSE) for small, moderate and large samples and for some values of the scale and the extension of Jeffrey’s prior parameters using the simulation techniques. Results: It turns out that the maximum likelihood method and Bayesian method with Jeffrey’s prior result in smaller MSE compared to others in all cases. Conclusion: Based on the results of the simulation, the maximum likelihood method and Bayesian method with Jeffrey’s prior are found to be the best with respect to MSE.
© 2011 Faris M. Al-Athari. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.