Compound truncated Poisson gamma distribution for understanding multimodal SAR intensities

Abstract

In recent years, many works have addressed the proposal of new probability models by theoretic and applied reasons. Specifically, mixture models have been indicated to describe phenomena whose resulting data impose high flexibility. One drawback of these tools is the high number of parameters involved, which implies hard inference procedures. To outperform this gap, we propose a new model that is able to describe multimodal behaviors with only three parameters, called compound truncated Poisson gamma (CTrPGa) distribution. Some properties of the CTrPGa law are derived and discussed: hazard, characteristic and cumulative functions and ordinary moments. Beyond, moment estimation, maximum likelihood estimation (via the expectation maximization algorithm) and empirical characteristic function methods for CTrPGa parameters are furnished. The first of them may be reduced to solve one nonlinear equation, which facilitates its use. We perform a simulation analysis to compare the performance of the three estimation methods studied. Moreover, since the gamma distribution and its mixture versions are commonly used to characterize synthetic aperture radar (SAR) intensities, we perform some real experiments with SAR imagery. The results present evidence that our model is a reasonable assumption that can be taken into account in the pre-processing step of such images.