Related papers: Exactly computing the tail of the Poisson-Binomial…
Mixed Poisson distributions provide a flexible approach to the analysis of count data with overdispersion, zero inflation, or heavy tails. Since the Poisson mean must be nonnegative, the mixing distribution is typically assumed to have…
The distribution of sum of independent non-identical binomial random variables is frequently encountered in areas such as genomics, healthcare, and operations research. Analytical solutions to the density and distribution are usually…
We develop a general technique for bounding the tail of the total variation distance between the empirical and the true distributions over countable sets. Our methods sharpen a deviation bound of Devroye (1983) for distributions over finite…
We report some properties of heavy-tailed Sibuya-like distributions related to thinning, self-decomposability and branching processes. Extension of the thinning operation of on-negative integer-valued random variables to scaling by…
Many management decisions involve accumulated random realizations for which only the first and second moments of their distribution are available. The sharp Chebyshev-type bound for the tail probability and Scarf bound for the expected loss…
By the modified directed likelihood, higher order accurate confidence limits for a scalar parameter are obtained from the likelihood. They are conveniently described in terms of a confidence distribution, that is a sample dependent…
We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.
We re-examine a lower-tail upper bound for the random variable $$X=\prod_{i=1}^{\infty}\min\left\{\sum_{k=1}^iE_k,1\right\},$$ where $E_1,E_2,\ldots\stackrel{iid}\sim\text{Exp}(1)$. This bound has found use in root-finding and seed-finding…
A wide range of natural and social phenomena result in observables whose distributions can be well approximated by a power-law decay. The well-known Hill estimator of the tail exponent provides results which are in many respects superior to…
This work proposes a novel method to robustly and accurately model time series with heavy-tailed noise, in non-stationary scenarios. In many practical application time series have heavy-tailed noise that significantly impacts the…
In this paper, we first use the distribution of the number of records to demonstrate that the right tail probabilities of counts of rare events are generally better approximated by the right tail probabilities of Poisson distribution than…
Given a finite collection of stochastic alternatives, we study the problem of sequentially allocating a fixed sampling budget to identify the optimal alternative with a high probability, where the optimal alternative is defined as the one…
In this article we study the tail probability of the mass of Gaussian multiplicative chaos. With the novel use of a Tauberian argument and Goldie's implicit renewal theorem, we provide a unified approach to general log-correlated Gaussian…
To accommodate numerous practical scenarios, in this paper we extend statistical inference for smoothed quantile estimators from finite domains to infinite domains. We accomplish the task with the help of a newly designed truncation…
A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…
We obtain in this paper using the saddle point method the expression for the exact asymptotic for the tail of maximum of smooth (twice continuous differentiable) random field (process) distribution.
The Markov Chain Monte Carlo (MCMC) algorithm is a widely recognised as an efficient method for sampling a specified posterior distribution. However, when the posterior is multi-modal, conventional MCMC algorithms either tend to become…
We derive simple but nearly tight upper and lower bounds for the binomial lower tail probability (with straightforward generalization to the upper tail probability) that apply to the whole parameter regime. These bounds are easy to compute…
The allocation problem for a $d$-dimensional Poisson point process is to find a way to partition the space to parts of equal size, and to assign the parts to the configuration points in a measurable, "deterministic" (equivariant) way. The…
Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…