Keywords and phrases: modified Bessel function of the third kind, generalized inverse Gaussian distribution, weighted distribution, finite mixture, EM-algorithm.
Received: April 11, 2021; Revised: October 23, 2021: Accepted: December 12, 2021; Published: December 27, 2021
How to cite this article: Calvin B. Maina, Patrick G. O. Weke, Carolyne A. Ogutu and Joseph A. M. Ottieno, EM-algorithm for a normal-weighted inverse Gaussian distribution: Normal-reciprocal inverse Gaussian distribution, Advances and Applications in Statistics 72 (2022), 1‑24. DOI: 10.17654/0972361722001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] K. Aas and H. Haff, NIG and Skew student’s t: Two special cases of the generalised hyperbolic, Norwegian Computing Center, 2005. [2] K. Aas and H. Haff, The generalised hyperbolic skew student’s t-distribution, Journal of Financial Econometrics 4(2) (2006), 275-309. [3] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Function, Dover, New York, 1972. [4] O. Barndorff-Nielsen, Exponentially decreasing distributions for the logarithm of particle size, Proc. R. Soc. Lond. A 353 (1977), 409-419. [5] O. Barndorff-Nielsen, Normal inverse Gaussian distribution and stochastic volatility modelling, Scandinavian Journal of Statistics 24 (1997), 1-13. [6] O. E. Barndorff-Nielsen and K. Prause, Apparent scaling, Finance and Stochastics 5 (2001), 103-113. [7] A. P. Dempster, N. M. Laird and D. Rubin, Maximum likelihood from incomplete data using the EM algorithm, Journal Roy. Statist. Soc. B 39 (1977), 1-38. [8] E. Eberlein and U. Keller, Hyperbolic distributions in finance, Bernoulli 1(3) (1995), 281-299. [9] R. A. Fisher, The Effect of Methods of Ascertainment upon the Estimation of Frequencies, The Annals of Human Genetics 1934. [10] R. C. Gupta and O. Akman, On reliability studies of a weighted inverse Gaussian distribution model, Statistical Papers 38 (1995), 445-452. [11] B. Jorgensen, V. Seshadri and G. A. Whitmore, On the mixture of inverse Gaussian distribution with its complementary reciprocal, Scandinavian Journal of Statistics 18 (1991), 77-89. [12] D. Karlis, An EM type algorithm for maximum likelihood estimation of the normal-inverse Gaussian distribution, Statistics and Probability Letters 57 (2002), 43-52. [13] G. P. Patil and C. R. Rao, Weighted distributions and size-biased sampling with applications to wildlife populations and human families, Biometrics 34 (1978), 179-189. [14] K. Prause, Modelling Financial Data using Generalized Hyperbolic Distributions, FDM preprint 48, University of Freiburg, 1999.
|