Related papers: Base Dependence of Benford Random Variables
The occurrence of first significant digits of numbers in large data is often governed by a logarithmically decreasing distribution called Benford's law (BL), reported first by S. Newcomb (SN) and many decades later independently by F.…
A phenomenological law, called Benford's law, states that the occurrence of the first digit, i.e., $1,2,...,9$, of numbers from many real world sources is not uniformly distributed, but instead favors smaller ones according to a logarithmic…
We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures, or belong to the…
Suppose that in a multiple choice examination the leading digit of the correct options follows Benford's Law, while the the leading digit of the distractors are uniform. Consider a strategy for guessing at answers that selects the option…
The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper…
Unlike classical and free independence, the boolean and monotone notions of independence lack of the property of independent constants. In the scalar case, this leads to restrictions for the central limit theorems, as observed by F.…
We consider a variant of Stern's diatomic sequence, studied recently by Northshield. We prove that this sequence $b$ is invariant under \emph{digit reversal} in base $3$, that is, $b_n=b_{n^R}$, where $n^R$ is obtained by reversing the…
The measurement of $B_s$-meson branching fractions is a fundamental tool to probe physics beyond the Standard Model. Every measurement of untagged time-integrated $B_s$-meson branching fractions is model-dependent due to the time dependence…
This study actually draws from and builds on an earlier paper (Kumar and Bhattacharya, 2002). Here we have basically added a neutrosophic dimension to the problem of determining the conditional probability that a financial fraud has been…
A new version of a strong law of large numbers for a ``good'' pairwise independent sequence of random variables (r.v.'s) with a small part of ``bad'' dependent r.v.'s is proposed. The main goal is to relax the assumption on the existence of…
In this paper, we focus on the problem of stable prediction across unknown test data, where the test distribution is agnostic and might be totally different from the training one. In such a case, previous machine learning methods might…
In many real life situations, it is observed that the first digits (i.e., $1,2,\ldots,9$) of a numerical data-set, which is expressed using decimal system, do not follow a random distribution. Instead, smaller numbers are favoured by nature…
It is known that increasing powers of a continuous random variable converge in distribution to Benford's law as the exponent approaches infinity. The rate of convergence has been estimated using Fourier analysis, but we present an…
We provide conditions on dependent and on non-stationary random variables $X_n$ ensuring that the mantissa of the sequence of products $\left(\prod_{1}^{n}X_k\right)$ is almost surely distributed following the Benford's law or converges in…
In this paper, we investigate parameter families of iterated function systems and continuity. Specifically, if we have a set of iterated function systems that depend continuously on a parameter, which properties of the invariant sets will…
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…
It is well known that while the independence of random variables implies zero correlation, the opposite is not true. Namely, uncorrelated random variables are not necessarily independent. In this note we show that the implication could be…
Given natural parameters s and r, where $2\leq s\leq r$, we consider the distribution of a random variable $\xi=\sum\limits_{k=1}^{\infty}s^{-k}\xi_k\equiv\Delta^{r_s}_{\xi_1\xi_2...\xi_k...},$ where $(\xi_k)$ is a sequence of independent…
We obtain an elementary invariance principle for multi-dimensional Brownian sheet where the underlying random fields are not necessarily independent or stationary. Possible applications include unit-root tests for spatial as well as panel…
Natural numbers which are nontrivial multiples of some permutation of their base-$b$ digit representations are called permutiples. Specific cases include numbers which are multiples of cyclic permutations (cyclic numbers) and reversals of…