The Gamma Generalized Normal Distribution: A Descriptor of SAR Imagery

We propose a new four-parameter distribution for modeling synthetic aperture radar (SAR) imagery named the gamma generalized normal (GGN) by combining the gamma and generalized normal distributions. A mathematical characterization of the new distribution is provided by identifying the limit behavior and by calculating the density and moment expansions. The GGN model performance is evaluated on both synthetic and actual data and, for that, maximum likelihood estimation and random number generation are discussed. The proposed distribution is compared with the beta generalized normal distribution (BGN), which has already shown to appropriately represent SAR imagery. The performance of these two distributions are measured by means of statistics which provide evidence that the GGN can outperform the BGN distribution in some contexts.

Beta Generalized Normal Distribution with an Application for SAR Image Processing

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.