Related papers: Bounds on Tail Probabilities in Exponential famili…

We show bounds on tail probabilities for quadratic forms in sub-gaussian non-necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of such forms. This will allow us to formulate the above-mentioned…

In this paper we establish lower bounds on information divergence from a distribution to certain important classes of distributions as Gaussian, exponential, Gamma, Poisson, geometric, and binomial. These lower bounds are tight and for…

We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. A simplified version of the bound that parametrizes the ``aggregating distribution'' using a certain pushforward of…

We define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns. The three distributions we consider are derived from the gamma-Poisson, gamma-negative binomial, and…

By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.

We consider a family of multivariate distributions with heavy-tailed margins and the type I elliptical dependence structure. This class of risks is common in finance, insurance, environmental and biostatistic applications. We obtain the…

The article is devoted to the study of exponential statistical structures of type B, which constitute a subclass of exponential families of probability distributions. This class is characterized by a number of analytical and probabilistic…

We use the properties of the Matuszewska indices to show asymptotic inequalities for hazard rates. We discuss the relation between membership in the classes of dominatedly or extended rapidly varying tail distributions and corresponding…

This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…

In risk theory, financial asset returns often follow heavy-tailed distributions. Investors and risk managers used to compare risk measures as the value at risk or tail value at risk in order over the whole confidence levels to avoid the…

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…

In this article, we introduce the notion of free subexponentiality, which extends the notion of subexponentiality in the classical probability setup to the noncommutative probability spaces under freeness. We show that distributions with…

In this article, we propose a new three parameter distribution by compounding negative binomial with reciprocal inverse Gaussian model called negative binomial-reciprocal inverse Gaussian distribution. This model is tractable with some…

Gamma distributions, which contain the exponential as a special case, have a distinguished place in the representation of near-Poisson randomness for statistical processes; typically, they represent distributions of spacings between events…

Tail risk measures are fully determined by the distribution of the underlying loss beyond its quantile at a certain level, with Value-at-Risk, Expected Shortfall and Range Value-at-Risk being prime examples. They are induced by law-based…

In this paper we present a tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that are not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing…

The proportional odds model gives a method of generating new family of distributions by adding a parameter, called tilt parameter, to expand an existing family of distributions. The new family of distributions so obtained is known as…

The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the…

Random matrices acting on structured sets play a fundamental role in high-dimensional geometry, compressed sensing, and randomized algorithms. Existing results primarily focus on subgaussian models, when random matrices act as…

We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational…