A proposal for a new method of classification of objects of various nature, named “2”-soft classification, which allows for referring objects to one of two types with optimal entropy probability for available collection of learning data with consideration of additive errors therein. A decision rule of randomized parameters and probability density function (PDF) is formed, which is determined by...

Many problems of enzyme kinetics can be described by a function known as the Michaelis-Menten (M-M) function. In this paper, motivated by the importance of Michaelis-Menten function in biochemistry and other biological phenomena, we have introduced a new class of generalized Pearson distribution arising from Michaelis-Menten function. Various properties of this distribution are derived, for exa...

The sum of correlated gamma random variables appears in the analysis of many wireless communications systems, e.g. in systems under Nakagami-m fading. In this Letter we obtain exact expressions for the probability density function (PDF) and the cumulative distribution function (CDF) of the sum of arbitrarily correlated gamma variables in terms of certain Lauricella functions. Index Terms Gamma ...

The implicit particle filter is a sequential Monte Carlo method for data assimilation. The idea is to focus the particles onto the high probability regions of the target probability density function (pdf) so that the number of particles required for a good approximation of this pdf remains manageable, even if the dimension of the state space is large. We explain how this idea is implemented, di...

The behavior of the probability density function (PDF) transport equation at the limits of the probability space is studied from the point of view of fluid mechanics. Different boundary conditions are considered depending on the nature of the variable considered (velocity, scalar, and position). A study of the implications of entrance and exit conditions is performed, showing that a new term sh...

In this work, a new technique for the estimation of the Shannon’s entropy and the Kullback-Leibler (KL) divergence for one dimensional data is presented. The estimator is based on the Szegö’s theorem for sequences of Toeplitz matrices, which deals with the asymptotic behavior of the eigenvalues of those matrices, and the analogy between a probability density function (PDF) and a power spectral ...

In this paper, we propose a steepest descent algorithm based on the natural gradient to design the controller of an open-loop stochastic distribution control system (SDCS) of multi-input and single output with a stochastic noise. Since the control input vector decides the shape of the output probability density function (PDF), the purpose of the controller design is to select a proper control i...

A simple statistical model of azimuthal and temporal dispersion in mobile radio channels is proposed. The model includes the probability density function (pdf) of the delay and azimuth of the impinging waves as well as their expected power conditioned on the delay and azimuth. The statistical properties are extracted from macrocellular measurements conducted in a variety of urban environments. ...