No abstract

Synthetic aperture radar (SAR) is an efficient and widely used remote sensing tool. However, data extracted from SAR images are contaminated with speckle, which precludes the application of techniques based on the assumption of additive and normally distributed noise. One of the most successful approaches to describing such data is the multiplicative model, where intensities can follow a variety of distributions with positive support. The G 0 I model is among the most successful ones. Although several estimation methods for the G 0 I parameters have been proposed, there is no work exploring a regression structure for this model. Such a structure could allow us to infer unobserved values from available ones. In this work, we propose a G 0 I regression model and use it to describe the influence of intensities from other polarimetric channels. We derive some theoretical properties for the new model: Fisher information matrix, residual measures, and influential tools. Maximum likelihood point and interval estimation methods are proposed and evaluated by Monte Carlo experiments. Results from simulated and actual data show that the new model can be helpful for SAR image analysis.

Based on the normal distribution, a new generator of continuous distributions is presented using the monotonic functions  and , such that  and  are the baselines. A study of identifiability of the proposed class is exhibited as well as the series expansions for its cumulative distribution function and probability density function. Additionally, some mathematical properties of the class are discussed, namely, the raw moments, the central moments, the moment generating function, the characteristic function, the derivatives of the log-likelihood function, and a study of the support.  A numerical analysis comprising a simulation study and an application to real data is presented. Comparisons between the proposed model and other well-known models evince its potentialities and modeling benefits.

In recent years various probability models have been proposed for describing lifetime data. Increasing model flexibility is often sought as a means to better describe asymmetric and heavy tail distributions. Such extensions were pioneered by the beta-G family. However, efficient goodness-of-fit (GoF) measures for the beta-G distributions are sought. In this paper, we combine probability weighted moments (PWMs) and the Mellin transform (MT) in order to furnish new qualitative and quantitative GoF tools for model selection within the beta-G class. We derive PWMs for the Fr\’{e}chet and Kumaraswamy distributions; and we provide expressions for the MT, and for the log-cumulants (LC) of the beta-Weibull, beta-Fr\’{e}chet, beta-Kumaraswamy, and beta-log-logistic distributions. Subsequently, we construct LC diagrams and, based on the Hotelling’s $T^2$ statistic, we derive confidence ellipses for the LCs. Finally, the proposed GoF measures are applied on five real data sets in order to demonstrate their applicability.