Abstract: The objective of this paper is to construct and obtain properties of a normal variance-mean mixture with as a mixing distribution. The parameters of the mixed model are estimated using the EM algorithm and the financial data used are from Range Resource Corporation (RRC).
The mixing distribution is a weighted inverse Gaussian distribution. The properties of the proposed model have been obtained via the properties of the mixing distribution. Five iterative schemes for the EM algorithm have been compared. The first scheme is based on explicit solution of the simultaneous (normal) equations. The other 4 do not depend on explicit solutions.
For all 5 cases, the estimates of the parameters of the mixture converge to the same corresponding values at tolerance level Also, for all 5 cases, iterations take less than 5 seconds for the data used. However, the number of iterations differs for each scheme.
It is, therefore, not necessary to solve simultaneous equations explicitly to estimate parameters via EM algorithm. The proposed model fits the data well. |
Keywords and phrases: modified Bessel function of the third kind, generalized inverse Gaussian distribution, weighted distribution, EM-algorithm, iterative schemes.
Received: April 17, 2021; Revised: October 17, 2021; Accepted: November 20, 2021; Published: December 21, 2021
How to cite this article: Calvin B. Maina, Patrick G. O. Weke, Carolyne A. Ogutu and Joseph A. M. Ottieno, Normal- mixture with application to financial data, Far East Journal of Theoretical Statistics 63(2) (2021), 93-125. DOI: 10.17654/0972086321003
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