Related papers: CDF of non-central $\chi^2$ distribution revisited…
FPSAC 2013 Extended Abstract. We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
Nonlocal QFT of one-component scalar field $\varphi$ in $D$-dimensional Euclidean spacetime is considered. The generating functional (GF) of complete Green functions $\mathcal{Z}$ as a functional of external source $j$, coupling constant…
In this note the use of the zero degree non-central chi squared distribution as predictive distribution for ensemble postprocessing is investigated. It has a point mass at zero by definition, and is thus particularly suited for…
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based…
We give an overview of published algorithms by our group and of current activities and future plans. In particular, we give details on methods for computing special functions and discuss in detail two current lines of research. Firstly, we…
We introduce a new basis of the non-commutative symmetric functions whose commutative images are Schur functions. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions…
The Friedman test has been extensively applied as a nonparametric alternative to the conventional F procedure for comparing treatment effects in randomized complete block designs. A chi-square distribution provides a convenient…
We introduce and study a generalization $s_{(\mu|\lambda)}$ of the Schur functions called the almost symmetric Schur functions. These functions simultaneously generalize the finite variable key polynomials and the infinite variable Schur…
A Wright function based framework is proposed to combine and extend several distribution families. The $\alpha$-stable distribution is generalized by adding the degree of freedom parameter. The PDF of this two-sided super distribution…
In this paper, we propose two new tests for testing the equality of the covariance functions of several functional populations, namely a quasi GPF test and a quasi $F_{\max}$ test. The asymptotic random expressions of the two tests under…
This work presents a novel approach to the mean-square analysis of the normalized least mean squares (NLMS) algorithm for circular complex colored Gaussian inputs. The analysis is based on the derivation of a closed-form expression for the…
We prove the following superexponential distribution inequality: for any integrable $g$ on $[0,1)^{d}$ with zero average, and any $\lambda>0$ \[ |\{ x \in [0,1)^{d} \; :\; g \geq\lambda \}| \leq e^{-…
We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From…
We extend the notion of convexity of functions defined on global nonpositive curvature spaces by introducing (geodesically) $h$-convex functions. We prove estimates of Hermite-Hadamard type via Katugampola's fractional integrals. We obtain…
In this paper, we derive closed-form exact expressions for the main statistics of the ratio of squared alpha-mu random variables, which are of interest in many scenarios for future wireless networks where generalized distributions are more…
In this short note, we introduce probabilistic Cauchy functional equations, specifically, functional equations of the following form: $$ f(X_1 + X_2) \stackrel{d}{=} f(X_1) + f(X_2), $$ where $X_1$ and $X_2$ represent two independent…
In this paper, we obtain various series and asymptotic expansions involving the modified Bessel function of the second kind for the normal inverse Gaussian cumulative distribution function. The new expansions accelerate computations,…
Approximate distributions for sum and difference of linearly correlated $\chi^{2}$ distributed random variables are derived. It is shown that they can be reduced to conveniently parametrized gamma and Variance-Gamma distributions,…
Let $F$ be the cumulative distribution function (CDF) of the base-$q$ expansion $\sum_{n=1}^\infty X_n q^{-n}$, where $q\ge2$ is an integer and $\{X_n\}_{n\geq 1}$ is a stationary stochastic process with state space $\{0,\ldots,q-1\}$. In a…