Beta generalized normal distribution with an application for SAR image processing

Abstract

In this paper, we introduce the beta generalized normal distribution, which is obtained by compounding the beta and generalized normal [S. Nadarajah, A generalized normal distribution, J. Appl. Stat. 32 (2005), pp. 685–694] 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, especially skewness and tail weights, due to two additional parameters. We obtain general expansions for the moments. We investigate the estimation of the parameters by maximum likelihood. We also propose a random number generator for the new distribution. We analyse and model actual synthetic aperture radars after the new distribution. The results could outperform the 0, Κ, and Γ distributions in several scenarios.