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  The log-likelihood and the posterior distributions have been constructed.

logistic mixture, modified Bessel function, rth moment, parametrization, posterior distribution, logistic inverse Gaussian.

Received: July 20, 2021; Revised: June 2, 2022; Accepted: July 19, 2022; Published: August 1, 2022

How to cite this article: Howard Omukami, Patrick Weke and Joseph Ottieno, The logistic inverse Gaussian (LIG) distribution, Far East Journal of Theoretical Statistics 65 (2022), 97-114. http://dx.doi.org/10.17654/0972086322008

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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