The Burr X Pareto Distribution: Properties, Applications and VaR Estimation

• Main Authors: Mustafa Ç. Korkmaz, Emrah Altun, Haitham M. Yousof, Ahmed Z. Afify, Saralees Nadarajah
• Format: Article
• Language: English
• Published: MDPI AG 2017-12-01
• Series: Journal of Risk and Financial Management
• Subjects: Burr X distribution; Pareto distribution; maximum likelihood estimation; heavy tail distribution; value-at-risk
• Online Access: https://www.mdpi.com/1911-8074/11/1/1

In this paper, a new three-parameter Pareto distribution is introduced and studied. We discuss various mathematical and statistical properties of the new model. Some estimation methods of the model parameters are performed. Moreover, the peaks-over-threshold method is used to estimate Value-at-Risk (VaR) by means of the proposed distribution. We compare the distribution with a few other models to show its versatility in modelling data with heavy tails. VaR estimation with the Burr X Pareto distribution is presented using time series data, and the new model could be considered as an alternative VaR model against the generalized Pareto model for financial institutions.