Related papers: Tight tail probability bounds for distribution-fre…
In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…
We present a novel approach to estimating discrete distributions with (potentially) infinite support in the total variation metric. In a departure from the established paradigm, we make no structural assumptions whatsoever on the sampling…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
We study the extent of independence needed to approximate the product of bounded random variables in expectation, a natural question that has applications in pseudorandomness and min-wise independent hashing. For random variables whose…
We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test…
There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the…
Chernoff's bound binds a tail probability (ie. $Pr(X \ge a)$, where $a \ge EX$). Assuming that the distribution of $X$ is $Q$, the logarithm of the bound is known to be equal to the value of relative entropy (or minus Kullback-Leibler…
The Chernoff bound is an important inequality relation in probability theory. The original version of the Chernoff bound is to give an exponential decreasing bound on the tail distribution of sums of independent random variables. Recent…
In this paper, we obtain some results on precise large deviations for non-random and random sums of widely dependent random variables with common dominatedly varying tail distribution or consistently varying tail distribution on…
Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter…
There is accumulating evidence in the literature that stability of learning algorithms is a key characteristic that permits a learning algorithm to generalize. Despite various insightful results in this direction, there seems to be an…
In this paper we present a method for obtaining tail-bounds for random variables satisfying certain probabilistic recurrences that arise in the analysis of randomized parallel divide and conquer algorithms. In such algorithms, some…
In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…
Our work aims to study the tail behaviour of weighted sums of the form $\sum_{i=1}^{\infty} X_{i} \prod_{j=1}^{i}Y_{j}$, where $(X_{i}, Y_{i})$ are independent and identically distributed, with common joint distribution bivariate Sarmanov.…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to…
For independent $X$ and $Y$ in the inequality $P(X\leq Y+\mu)$, we give sharp lower bounds for unimodal distributions having finite variance, and sharp upper bounds assuming symmetric densities bounded by a finite constant. The lower bounds…
In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…
Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…
Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds…