Related papers: Hypergeometric tail inequalities: ending the insan…

We revisit and refine known tail inequalities and confidence bounds for the hypergeometric distribution, i.e., for the setting where we sample without replacement from a fixed population with binary values or properties. The results are…

Let $n,k$ be positive integers such that $n\geq k$, and let $H$ be a hypergeometric random variable counting the number of black marbles in a sample without replacement of size $k$ from an urn that contains $i\in \{1,\ldots, n\}$ black and…

The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…

The authors announce a general tail estimate, called a decoupling inequality, for a symmetrized sum of non-linear $k$-correlations of $n>k$ independent random variables.

We use a simple method to derive two concentration bounds on the hypergeometric distribution. Comparison with existing results illustrates the advantage of these bounds across different regimes.

We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.

The Gini index underestimates inequality for heavy-tailed distributions: for example, a Pareto distribution with exponent 1.5 (which has infinite variance) has the same Gini index as any exponential distribution (a mere 0.5). This is…

We study probability inequalities leading to tail estimates in a general semigroup $\mathscr{G}$ with a translation-invariant metric $d_{\mathscr{G}}$. (An important and central example of this in the functional analysis literature is that…

Several new identities for elliptic hypergeometric series are proved. Remarkably, some of these are elliptic analogues of identities for basic hypergeometric series that are balanced but not very-well-poised.

The normal distribution and its perturbation has left an immense mark on the statistical literature. Hence, several generalized forms were developed to model different skewness, kurtosis, and body shapes. However, it is not easy to…

The approach used by Kalashnikov and Tsitsiashvili for constructing upper bounds for the tail distribution of a geometric sum with subexponential summands is reconsidered. By expressing the problem in a more probabilistic light, several…

Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…

In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as…

In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…

This paper presents compact notations for concentration inequalities and convenient results to streamline probabilistic analysis. The new expressions describe the typical sizes and tails of random variables, allowing for simple operations…

This note provides some new inequalities and approximations for beta distributions, including tail inequalities, exponential inequalities of Hoeffding and Bernstein type, Gaussian inequalities and approximations.

Let $\{X_i\}_{i\geq1}$ be an i.i.d. sequence of random variables and define, for $n\geq2$, \[T_n=\cases{n^{-1/2}\hat{\sigma}_n^{-1}S_n,\quad \hat{\sigma}_n>0,\cr 0,\quad \hat{\sigma}_n=0,}with S_n=\sum_{i=1}^nX_i,…

In every finite mixture of different normal distributions, there will always be exactly one of those distributions that not only is over-represented in the right tail of the mixture, but even completely overwhelms all other subpopulations…

This article describes mathematical methods for estimating the top-tail of the wealth distribution and therefrom the share of total wealth that the richest $p$ percent hold, which is an intuitive measure of inequality. As the data base for…

We generalize a famous tail Doob's inequality, relative two non-negative random variables, arising in the martingale theory, in two directions: on the more general source data and on the random variables belonging to the so-called Grand…