A theoretical framework for Landsat data modeling based on the matrix variate mean-mixture of normal model

Area of Science:

• Statistics
• Probability Theory
• Matrix Variate Distributions

Background:

• The analysis of matrix-valued data requires flexible distributional models.
• Existing models may not capture the complexity inherent in multivariate matrix data.

Purpose of the Study:

• Introduce a novel family of matrix variate distributions.
• Investigate the fundamental properties of this new distribution family.
• Demonstrate the practical application of the proposed distributions.

Main Methods:

• Development of a new matrix variate distribution based on mean-mixture of normal (MMN) models.
• Investigation of stochastic representation, moments, characteristic function, and marginal/conditional distributions.
• Implementation of an EM-type algorithm for parameter estimation via maximum likelihood.

Main Results:

• A new flexible family of matrix variate distributions is proposed.
• Properties such as stochastic representation, moments, and conditional distributions are derived.
• Special cases including restricted skew-normal, exponentiated MMN, and mixed-Weibull MMN distributions are presented.
• The EM-type algorithm facilitates parameter estimation.

Conclusions:

• The proposed matrix variate distribution family offers a versatile tool for statistical modeling.
• The methodology is validated through simulation studies and real-world satellite data analysis.
• This work contributes a new framework for analyzing matrix-structured data in various scientific domains.