Beta Generalized Normal Distribution with an Application for SAR Image Processing

TL;DR

This paper introduces the beta generalized normal distribution, a flexible new model with applications in SAR image processing, demonstrating its advantages over existing models in modeling radar data.

Contribution

The paper proposes a novel beta generalized normal distribution, including methods for parameter estimation and random number generation, with applications to SAR image analysis.

Findings

Outperforms $ ext{G}^0$, $ ext{K}$, and $ ext{ extGamma}$ distributions in SAR data modeling

Provides flexible skewness and tail weight modeling

Includes methods for parameter estimation and simulation

Abstract

We introduce the beta generalized normal distribution which is obtained by compounding the beta and generalized normal [Nadarajah, S., A generalized normal distribution, \emph{Journal of Applied Statistics}. 32, 685--694, 2005] distributions. The new model includes as sub-models the beta normal, beta Laplace, normal, and Laplace distributions. The shape of the new distribution is quite flexible, specially the skewness and the tail weights, due to two additional parameters. We obtain general expansions for the moments. The estimation of the parameters is investigated by maximum likelihood. We also proposed a random number generator for the new distribution. Actual synthetic aperture radar were analyzed and modeled after the new distribution. Results could outperform the $\mathcal{G}^0$, $\mathcal{K}$, and $\Gamma$ distributions in several scenarios.