Let ρ(x, t) denote a family of probability density functions parameterized by time t. We show the existence of a family {τt : t > 0} of deterministic nonlinear (chaotic) point transformations whose invariant probability density functions are precisely ρ(x, t). In particular, we are interested in the densities that arise from the diffusions. We derive a partial differential equation whose soluti...

Mixture probability density functions had recently been proposed to describe some fertility patterns characterized by a bi-modal shape. These mixture probability density functions appear to be adequate when the fertility pattern is actually bi-modal but less useful when the shape of age-specific fertility rates is unimodal. A further model is proposed based on skew-symmetric probability density...

Fisher distance based Genetic Algorithm: GA clustering method which takes into account overlapped space among probability density functions of clusters in feature space is proposed. Through experiments with simulation data of 2D and 3D feature space generated by random number generator, it is found that clustering performance depends on overlapped space among probability density function of clu...

Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical ...

Based on probability density evolution method (PDEM) and Bayes’ law, a new filter strategy is proposed, in which the prior of system state interest predicted by solving generalized equation (GDEE), posterior then updated terms Bayesian formula. Furthermore, Chebyshev polynomial-based collocation developed to obtain numerical solutions probability. Three illustrative examples are finally present...

In this paper kernel estimates of the joint and conditional probability density functions are used to generate synthetic streamflow sequences. Streamflow is assumed to be a Markov process with time dependence characterized by a multivariate probability density function. Kernel methods are used to estimate this multivariate density function. Simulation proceeds by sequentially resampling from th...

 The ratio of independent random variables arises in many applied problems. In this article, the distribution of the ratio X/Y is studied, when X and Y are independent Rice random variables. Ratios of such random variable have extensive applications in the analysis of noises of communication systems. The exact forms of probability density function (PDF), cumulative distribution function (CDF) a...

This paper analyzes the distribution and density functions of the probability of error for Rayleigh and Rician fading channels with diversity. An expression for the signal-to-noise ratio is derived for an asynchronous CDMA (A-CDMA) system with diversity. The error probability distribution and density functions are derived and plotted for different mean energy-to-noise ratios.