Related papers: Acknowledgment of priority: Usage of the Lambert W…
In upcoming papers by Conrey, Farmer and Zirnbauer there appear conjectural formulas for averages, over a family, of ratios of products of shifted L-functions. In this paper we will present various applications of these ratios conjectures…
In this article, we provide a comprehensive analysis of the asymptotic behavior of Bell numbers, enhancing and unifying various results previously dispersed in the literature. We establish several explicit lower and upper bounds. The main…
Likelihood ratio tests and the Wilks theorems have been pivotal in statistics but have rarely been explored in network models with an increasing dimension. We are concerned here with likelihood ratio tests in the $\beta$-model for…
The meaning of randomization tests has become obscure in statistics education and practice over the last century. This article makes a fresh attempt at rectifying this core concept of statistics. A new term -- "quasi-randomization test" --…
Likelihood ratio tests are a widely used method in global analyses in particle physics. The computation of the statistical significance (p-value) of these tests is usually done with a simple formula that relies on Wilks' theorem. There are,…
I present a parametric, bijective transformation to generate heavy tail versions Y of arbitrary RVs X ~ F. The tail behavior of the so-called 'heavy tail Lambert W x F' RV Y depends on a tail parameter delta >= 0: for delta = 0, Y = X, for…
The Laplace transform is a useful and powerful analytic tool with applications to several areas of applied mathematics, including differential equations, probability and statistics. Similarly to the inversion of the Fourier transform,…
After defining in detail the Lambert $W$-function branches, we give a large number of exact identities involving (infinite) symmetric functions of these branches, as well as geometrically convergent series for all the branches. In doing so,…
Logarithmic transformation of the data has been recommended by the literature in the case of highly skewed distributions such as those commonly found in information science. The purpose of the transformation is to make the data conform to…
Annotated bibliography of 18th, 19th, and early 20th century works involving Lambert series. A tour of 19th and early 20th century analytic number theory.
Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…
Let $X$ be lognormal$(\mu,\sigma^2)$ with density $f(x)$, let $\theta>0$ and define ${L}(\theta)=E e^{-\theta X}$. We study properties of the exponentially tilted density (Esscher transform) $f_\theta(x) =e^{-\theta x}f(x)/{L}(\theta)$, in…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…
In this paper new test statistics are introduced and studied for the important problem of testing hypothesis that involves inequality constraint on proportions when the sample comes from independent binomial random variables: Wald type and…
To decide upon the arithmetic nature of some numbers may be a non-trivial problem. Some cases are well know, for example exp(1) and W(1), where W is the Lambert function, are transcendental numbers. The Tsallis q-exponential, e_q (z), and…
On one hand, a large class of inequality measures, which includes the generalized entropy, the Atkinson, the Gini, etc., for example, has been introduced in Mergane and Lo (2013). On the other hand, the influence function of statistics is…
Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…
Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…
The zero bias distribution $W^*$ of $W$, defined though the characterizing equation $\mathit{EW}f(W)=\sigma^2Ef'(W^*)$ for all smooth functions $f$, exists for all $W$ with mean zero and finite variance $\sigma^2$. For $W$ and $W^*$ defined…
In this paper we propose an ad-hoc construction of the Likelihood Function, in order to develop a data analysis procedure, to be applied in atomic and nuclear spectral analysis. The classical Likelihood Function was modified taking into…