Related papers: Computation of the Generalized F Distribution
We compute the variances of sums in arithmetic progressions of generalised k-divisor functions related to certain L-functions in $\mathbb{F}_q(t)$, in the limit as $q\to\infty$. This is achieved by making use of recently established…
This application of nonstandard analysis utilizes the notion of the highly-staturated enlargement. These nonstandard methods clarify many aspects of the theory of generalized functions (distributions).
Recently we constructed a renormalizable field theory up to two loops for the quasi-static depinning of elastic manifolds in a disordered environment. Here we explore further properties of the theory. We show how higher correlation…
In this note, we establish the convergence in distribution of the maxima of i.i.d. random variables to the Gumbel distribution with the associated normalizing sequences for several examples that are related to the normal distribution.…
This paper develops a general methodology to conduct statistical inference for observations indexed by multiple sets of entities. We propose a novel multiway empirical likelihood statistic that converges to a chi-square distribution under…
An integral over the interval $(0,\pi)$ is given for the cumulative distribution function of a sum of independent gamma random variables with different scale and shape parameters. The cumulative distribution function of a positive definite…
Closed-form expressions for the distributions of the order statistics on the spacings between order statistics for the uniform distribution are obtained. This generalizes a result by Fisher concerning tests of significance in the harmonic…
We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. The main result is the…
We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier…
Dyadic shifts of point distributions in the multi-dimensional unit cube are considered as a randomization. Explicit formulas for the discrepancies of such randomized distributions are given in the paper in terms of Rademacher functions.…
In this paper, we obtain an upper bound for the Gini mean difference based on mean, variance and correlation for the case when the variables are correlated. We also derive some closed-form expressions for the Gini mean difference when the…
The noncentral $t$-distribution is a generalization of the Student's $t$-distribution. In this paper we suggest an alternative approach for computing the cumulative distribution function (CDF) of the noncentral $t$-distribution which is…
Using a common technique for approximating distributions [generalized functions], we are able to use standard Monte Carlo methods to compute QFT quantities in Minkowski spacetime, under phase transitions, or when dealing with coalescing…
We study the distribution functions of several classical error terms in analytic number theory, focusing on the remainder term in the Dirichlet divisor problem $\Delta(x)$. We first bound the discrepancy between the distribution function of…
The evolution of polarized quark distribution functions is taken into account the gluon emission and absorption, quark pair production and annihilation processes and treated by a statistical method which provides quark distribution…
We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the…
For Dirichlet characters $\chi$ mod $k$ where $k\geq 3$, we here give a computable formula for evaluating the mean square sums $\sum\limits_{\substack{\chi \text{ mod }k\\\chi(-1)=(-1)^r}}|L(r,\chi)|^2$ for any positive integer $r\geq 3$.…
In this paper, we consider the problem of estimating the density function of a Chi-squared variable on the basis of observations of another Chi-squared variable and a normal variable under the Kullback-Leibler divergence. We assume that…
First we generalize a famous lemma of Gallagher on the mean square estimate for exponential sums by plugging a weight in the right hand side of Gallagher's original inequality. Then we apply it in the special case of the Cesaro weight, in…
Linear regression with normally distributed errors - including particular cases such as ANOVA, Student's t-test or location-scale inference - is a widely used statistical procedure. In this case the ordinary least squares estimator…