Aims. Rotational speed is an important physical parameter of stars, and knowing the distribution of stellar rotational velocities is essential for understanding stellar evolution. However, rotational speed cannot be measured directly and is instead the convolution between the rotational speed and the sine of the inclination angle v sin i. Methods. We developed a method to deconvolve this inverse problem and obtain the cumulative distribution function for stellar rotational velocities extending the work of Chandrasekhar & Münch (1950, ApJ, 111, 142) Results. This method is applied: a) to theoretical synthetic data recovering the original velocity distribution with a very small error; and b) to a sample of about 12.000 field main-sequence stars, corroborating that the velocity distribution function is non-Maxwellian, but is better described by distributions based on the concept of maximum entropy, such as Tsallis or Kaniadakis distribution functions. Conclusions. This is a very robust and novel method that deconvolves the rotational velocity cumulative distribution function from a sample of v sin i data in a single step without needing any convergence criteria.

In this paper, we analyze several strategies for the estimation of the roughness parameter of the G 0 I distribution. It has been shown that this distribution is able to characterize a large number of targets in monopolarized synthetic aperture radar (SAR) imagery, deserving the denomination of "Universal Model." It is indexed by three parameters: 1) the number of looks (which can be estimated in the whole image); 2) a scale parameter; and 3) the roughness or texture parameter. The latter is closely related to the number of elementary backscatters in each pixel, one of the reasons for receiving attention in the literature. Although there are efforts in providing improved and robust estimates for such quantity, its dependable estimation still poses numerical problems in practice. We discuss estimators based on the minimization of stochastic distances between empirical and theoretical densities and argue in favor of using an estimator based on the triangular distance and asymmetric kernels built with inverse Gaussian densities. We also provide new results regarding the heavy-tailedness of this distribution.

Aims. Knowing the distribution of stellar rotational velocities is essential for understanding stellar evolution. Because we measure the projected rotational speed v sin i, we need to solve an ill-posed problem given by a Fredholm integral of the first kind to recover the "true" rotational velocity distribution. Methods. After discretization of the Fredholm integral we apply the Tikhonov regularization method to obtain directly the probability distribution function for stellar rotational velocities. We propose a simple and straightforward procedure to determine the Tikhonov parameter. We applied Monte Carlo simulations to prove that the Tikhonov method is a consistent estimator and asymptotically unbiased.Results. This method is applied to a sample of cluster stars. We obtain confidence intervals using a bootstrap method. Our results are in close agreement with those obtained using the Lucy method for recovering the probability density distribution of rotational velocities. Furthermore, Lucy estimation lies inside our confidence interval. Conclusions. Tikhonov regularization is a highly robust method that deconvolves the rotational velocity probability density function from a sample of v sin i data directly without the need for any convergence criteria.

Aims. It is important to know the binary mass-ratio distribution to better understand the evolution of stars in binary systems and to constrain their formation. However, in most cases, that is, for single-lined spectroscopic binaries, the mass ratio cannot be measured directly, but can only be derived as the convolution of a function that depends on the mass ratio and on the unknown inclination angle of the orbit on the plane of the sky. Methods. We extend our previous method for deconvolving this inverse problem by obtaining the cumulative distribution function (CDF) for the mass-ratio distribution as an integral. Results. After a suitable transformation of variables, this problem becomes the same as the problem of rotational velocities v sin i, allowing a close analytic formulation for the CDF. We here apply our method to two real datasets: a sample of Am star binary systems, and a sample of massive spectroscopic binaries in the Cyg OB2 association. Conclusions. We are able to reproduce previous results for the sample of Am stars. In addition, the mass-ratio distribution of massive stars shows an excess of systems with a low mass ratio, in contrast to what was claimed elsewhere. Our method proves to be very reliable and deconvolves the distribution from a sample in one single step.

Remotely sensed data are essential for understanding environmental dynamics, for their forecasting, and for early detection of disasters. Microwave remote sensing sensors complement the information provided by observations in the optical spectrum, with the advantage of being less sensitive to adverse atmospherical conditions and of carrying their own source of illumination. On the one hand, new generations and constellations of Synthetic Aperture Radar (SAR) sensors provide images with high spatial and temporal resolution and excellent coverage. On the other hand, SAR images suffer from speckle noise and need specific models and information extraction techniques. In this sense, the G0 family of distributions is a suitable model for SAR intensity data because it describes well areas with different degrees of texture. Information theory has gained a place in signal and image processing for parameter estimation and feature extraction. Entropy stands out as one of the most expressive features in this realm. We evaluate the performance of several parametric and non-parametric Shannon entropy estimators as input for supervised and unsupervised classification algorithms. We also propose a methodology for fine-tuning non-parametric entropy estimators. Finally, we apply these techniques to actual data.