A Normal Weighted Inverse Gaussian Distribution for Skewed and Heavy-Tailed Data

Calvin B.  Maina; Patrick G. O.  Weke; Carolyne A.  Ogutu; Joseph A. M.  Ottieno

doi:10.4236/am.2022.132013

Calvin B. Maina¹^*, Patrick G. O. Weke², Carolyne A. Ogutu², Joseph A. M. Ottieno²

Abstract: High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, various flexible distributions have been proposed. It is well known that mixture distributions produce flexible models with good statistical and probabilistic properties. In this work, a finite mixture of two special cases of Generalized Inverse Gaussian distribution has been constructed. Using this finite mixture as a mixing distribution to the Normal Variance Mean Mixture we get a Normal Weighted Inverse Gaussian (NWIG) distribution. The second objective, therefore, is to construct and obtain properties of the NWIG distribution. The maximum likelihood parameter estimates of the proposed model are estimated via EM algorithm and three data sets are used for application. The result shows that the proposed model is flexible and fits the data well.

Keywords: Inverse Gaussian, Finite Mixture, Weighted Distribution, Mixed Model, EM-Algorithm

Cite this paper: Maina, C. , Weke, P. , Ogutu, C. and Ottieno, J. (2022) A Normal Weighted Inverse Gaussian Distribution for Skewed and Heavy-Tailed Data. Applied Mathematics, 13, 163-177. doi: 10.4236/am.2022.132013.

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