November 2021 Matrix-variate Lindley distributions and its applications
Mariem Tounsi, Mouna Zitouni
Author Affiliations +
Braz. J. Probab. Stat. 35(4): 721-748 (November 2021). DOI: 10.1214/21-BJPS504

Abstract

Restring on the fact that the definition of multivariate analogs of the real gamma distribution is replaced by the Wishart distribution on symmetric matrices, and based on the notion of mixture models which is a flexible and powerful tool for treating data taken from multiple subpopulations, we set forward a multivariate analog of the real Lindley distributions of the first and second kinds on the modern framework of symmetric cones which can be used to model waiting and survival times matrix data. Within this framework, we first construct a new probability distributions, named the matrix-variate Lindley distributions. Some fundamental properties of these new distributions are established. Their statistical properties including moments, the coefficient of variation, skewness and the kurtosis are discussed. We then create an iterative hybrid Expectation-Maximization Fisher-Scoring (EM-FS) algorithm to estimate the parameters of the new class of probability distributions. Through simulation as well as comparative studies with respect to the Wishart distribution, the effectiveness and reliability of the proposed distributions are proved. Finally, the usefulness and the applicability of the new models are elaborated and illustrated by means of two real data sets from biological sciences and medical image segmentation which is one of the most important and popular tasks in medical image analysis.

Acknowledgement

The authors wish to thank the Editor and the Referees for valuable comments and suggestions which greatly improved the paper.

Citation

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Mariem Tounsi. Mouna Zitouni. "Matrix-variate Lindley distributions and its applications." Braz. J. Probab. Stat. 35 (4) 721 - 748, November 2021. https://doi.org/10.1214/21-BJPS504

Information

Received: 1 October 2020; Accepted: 1 May 2021; Published: November 2021
First available in Project Euclid: 13 December 2021

MathSciNet: MR4350957
zbMATH: 07477282
Digital Object Identifier: 10.1214/21-BJPS504

Keywords: expectation-maximization algorithm , Fisher-Scoring algorithm , Lindley probability distribution , Mixture models , Wishart probability distribution

Rights: Copyright © 2021 Brazilian Statistical Association

Vol.35 • No. 4 • November 2021
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