The problem of calculating the probability density and distribution function a strictly stable law is considered at x→0. expansions these values into power series were obtained to solve this problem. It was shown that in case α<1, asymptotic x→0; α>1, they convergent; α=1 domain |x|<1, converged an asymmetric Cauchy distribution. has been x→0 can be successfully used calculate laws.

In this article, we have suggested the three-parameter half-Cauchy Chen distribution which has been derived by compounding a continuous with family of distribution. The hazard rate function (HRF), quantile function, reversed survival cumulative (CDF), probability density (PDF), kurtosis, and skewness are some its statistical properties characteristics that explored. Utilizing methods LSE, CVM, ...

Additive fuzzy systems can filter impulsive noise from signals. Alpha-stable statistics model the impulsiveness as a parametrized family of probability density functions or unit-area bell curves. The bell-curve parameter ct ranges through the interval (0, 2] and gives the Gaussian bell curve when 0t = 2 and gives the Cauchy bell curve when ~t = 1. The impulsiveness grows as ~ falls and the bell...

We propose a method of estimation of the derivatives of probability density based on wavelets methods for a sequence of random variables with a common one-dimensional probability density function and obtain an upper bound on Lp-losses for such estimators. We suppose that the process is strongly mixing and we show that the rate of convergence essentially depends on the behavior of a special quad...

In this paper, we show that the Chapman-Kolmogorov formula could be used as a recursive formula for computing the m-step-ahead conditional density of a Markov bilinear model. The stationary marginal probability density function of the model may be approximated by the m-step-ahead conditional density for sufficiently large m.