相关论文: High moments Jarque-Bera tests for arbitrary distr…
Data from e+e-annihilation into hadrons collected by the JADE experiment at centre-of-mass energies between 14 GeV and 44 GeV were used to study moments of event shape distributions and the four-jet rate as a function of the Durham…
In this paper, a new mixture family of multivariate normal distributions, formed by mixing multivariate normal distribution and skewed distribution, is constructed. Some properties of this family, such as characteristic function, moment…
Every observation may follow a distribution that is randomly selected in a class of distributions. It is called the distribution uncertainty. This is a fact acknowledged in some research fields such as financial risk measure. Thus, the…
The validity of the strong law of large numbers for multiple sums $S_n$ of independent identically distributed random variables $Z_k$, $k\leq n$, with $r$-dimensional indices is equivalent to the integrability of $|Z|(\log^+|Z|)^{r-1}$,…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…
We consider parametric hypotheses testing for multidimensional ergodic diffusion processes observed at discrete time. We propose a family of test statistics, related to the so called $\phi$-divergence measures. By taking into account the…
Most normality tests in the literature are performed for scalar and independent samples. Thus, they become unreliable when applied to colored processes, hampering their use in realistic scenarios.We focus on Mardia's multivariate kurtosis,…
The supremum of the standardized empirical process is a promising statistic for testing whether the distribution function $F$ of i.i.d. real random variables is either equal to a given distribution function $F_0$ (hypothesis) or $F \ge F_0$…
For $a/q\in\mathbb{Q}$ the Estermann function is defined as $D(s,a/q):=\sum_{n\geq1}d(n)n^{-s}\operatorname{e}(n\frac aq)$ if $\Re(s)>1$ and by meromorphic continuation otherwise. For $q$ prime, we compute the moments of $D(s,a/q)$ at the…
It is well known that the approximate distribution of the usual test statistic of a goodness-of-fit test is chi-square, with degrees of freedom equal to the number of categories minus 1 (assuming that no parameters are to be estimated --…
We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate, absolutely continuous, or continuously…
We obtain conditional upper bounds for negative discrete moments of the derivative of the Riemann zeta-function averaged over a subfamily of zeros of the zeta function which is expected to have full density inside the set of all zeros. For…
A/B testing refers to the task of determining the best option among two alternatives that yield random outcomes. We provide distribution-dependent lower bounds for the performance of A/B testing that improve over the results currently…
This study develops two robust, quantile-sliced moment systems, mean and median absolute deviation (MAD and MedAD moments), to serve as foundational tools in parametric modeling, statistical inference, and describing distributional…
Let $X_{nr}$ be the $r$th largest of a random sample of size $n$ from a distribution $F (x) = 1 - \sum_{i = 0}^\infty c_i x^{-\alpha - i \beta}$ for $\alpha > 0$ and $\beta > 0$. An inversion theorem is proved and used to derive an…
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests…
We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…
We obtain new closed-form formulas for the moments and absolute moments of the variance-gamma distribution. We thus deduce new formulas for the moments and absolute moments of the product of two correlated zero mean normal random variables.
Distributions of strictly positive numbers are common and can be characterized by standard statistical measures such as mean, standard deviation, and skewness. We demonstrate that for these distributions the skewness $D_3$ is bounded from…
The search for remnants of the QCD chiral critical point is a central objective of current and future high-energy ion collision experiments. Previous studies suggest that a scaling law relating higher-order factorial moments of hadron…