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THE LOGISTIC INVERSE GAUSSIAN (LIG) DISTRIBUTION
Keywords:
logistic mixture, modified Bessel function, rth moment, parametrization, posterior distribution, logistic inverse GaussianDOI:
https://doi.org/10.17654/0972086322008Abstract
This paper examines the construction and properties of the logistic inverse Gaussian distribution (a new distribution which has been proposed) using the generalized inverse Gaussian as a mixed distribution in a logistic mixture. The derivation is based on the properties of modified Bessel function of the third kind as a special function and transformations from the Barndorff-Nielsen and Jorgensen parametrizations.
It has been established that the logistic inverse Gaussian is a special case of the logistic generalized inverse Gaussian when $\lambda = - \frac{1}{2}$. The log-likelihood and the posterior distributions have been constructed.
Received: July 20, 2021
Revised: June 2, 2022
Accepted: July 19, 2022
References
K. O. Nyawade, Generalized inverse Gaussian distributions under different parametrizations, Master Project in Mathematical Statistics, UoN-Kenya, 2018.
O. E. Barndorff-Nielsen and C. Halgreen, Infinite divisibility of the hyperbolic and generalized inverse Gaussian distributions, Z. Wahrsch. Verw. Geb. 38 (1977), 309-311.
A. P. Dempester, N. M. Laird and D. B. Rubin, Maximum Likelihood from incomplete data via EM algorithm, J. Roy. Statist. Soc. Ser. B 39(1) (1977), 1-38.
M. Konstantinos and S. Aaron, Maximum likelihood estimation of VARMA models using a state space EM algorithm, J. Time Ser. Anal. 28 (2007), 666-685.
E. Halphen, Sur un nouveau type de courbe de frequence, Comptes Rendus del’Academie de Sciences 213 (1941), 633-635.
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