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

[1]   Barndorff-Nielsen, O.E. (1977) Exponentially Decreasing Distributions for the Logarithm of Particle Size. Proceedings of the Royal Society A, 353, 409-419.
https://doi.org/10.1098/rspa.1977.0041

[2]   Barndorff-Nielsen, O.E. (1997) Normal Inverse Gaussian Distribution and Stochastic Volatility Modelling. Scandinavian Journal of Statistics, 24, 1-13.
https://doi.org/10.1111/1467-9469.00045

[3]   Fisher, R.A. (1934) The Effect of Methods of Ascertainment upon the Estimation of Frequencies. Annals of Eugenics, 6, 13-25.
https://doi.org/10.1111/j.1469-1809.1934.tb02105.x

[4]   Patil, G.P. and Rao, C.R. (1978) Weighted Distributions and Size-Biased Sampling with Applications to Wildlife Populations and Human Families. Biometrics, 34, 179-189.
https://doi.org/10.2307/2530008

[5]   Gupta, R.C. and Kundu, D. (2011) Weighted Inverse Gaussian—A Versatile Lifetime Model. Journal of Applied Statistics, 38, 2695-2708.
https://doi.org/10.1080/02664763.2011.567251

[6]   Dempster, A.P., Laird, N.M. and Rubin, D. (1977) Maximum Likelihood from Incomplete Data Using the EM Algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39, 1-38.
https://doi.org/10.1111/j.2517-6161.1977.tb01600.x

[7]   Karlis, D. (2002) An EM Type Algorithm for Maximum Likelihood Estimation of the Normal-Inverse Gaussian Distribution. Statistics and Probability Letters, 57, 43-52.
https://doi.org/10.1016/S0167-7152(02)00040-8

[8]   Kostas, F. (2007) Tests of Fit for Symmetric Variance Gamma Distributions. UADPhilEcon, National and Kapodistrian University of Athens, Greece.

Top