Adaptive systems rely on recursive estimation of a firmly bounded complexity. As a rule, they have to use an approximation of the posterior probability density function (pdf), which comprises unreduced information about the estimated parameter. In recursive setting, the latest approximate pdf is updated using the learnt system model and the newest data and then approximated. The fact that appro...

Recent analytical and numerical work have shown that the spectrum of the random non-hermitean Hamiltonian on a ring which models the physics of vortex line pinning in superconductors is one dimensional. In the maximally nonhermitean limit, we give a simple “one-line” proof of this feature. We then study the spectral curves for various distributions of the random site energies. We find that a cr...

*Correspondence: [email protected] 3Departamento de Estatística, Universidade Federal de Pernambuco, PE 50740-540, Recife, Brazil Full list of author information is available at the end of the article Abstract We propose and study a new compounded model to extend the half-Cauchy and power-Cauchy distributions, which offers more flexibility in modeling lifetime data. The proposed model is ...

cannot be a probability density function. To see this, note 2x− x = −x(x− √ 2)(x+ √ 2). If C = 0, then f(x) = 0 for all x, so ∫∞ −∞ f(x) = 0, but every probability density function has ∫∞ −∞ f(x) = 1. If C > 0, then f(x) < 0 on the range x ∈ (0, √ 2), but every probability density function has f(x) ≥ 0 for all x. If C < 0, then f(x) < 0 on the range x ∈ ( √ 2, 5/2), but every probability densit...

The abstract Cauchy problem for the non-stationary bulk queue M(t)|M[k, B]|1 Abstract We derived state probability equations describing the queue M (t)| M [k, B]|1 and formulated as an abstract Cauchy problem to investigate by means of the semi-group theory of bounded linear operators in functional analysis. With regard to the abstract Cauchy problem of this queue, we determined the eigenfuncti...

the probability density functions fitting to the discrete probability functions has always been needed, and very important. this paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. the main key in these fittings is the use of the derivative concept and common differential ...