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Let $(X_i)_{1 \le i \le n}$ be independent and identically distributed (i.i.d.) standard Gaussian random variables, and denote by $X_{(n)} = \max_{1 \le i \le n} X_i$ the maximum order statistic. It is well-known in extreme value theory…
We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…
This work continues the analysis of large deviations for randomly connected neural networks models of the brain. The originality of the model relies on the fact that the directed impact of one particle onto another depends on the state of…
Another new family of continuous probability distribution is proposed by using Generalized Marshal-Olkin distribution as the base line distribution in the Kumaraswamy-G distribution. This family includes (Cordeiro and de Castro, 2011) and…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
We explore negative dependence and stochastic orderings, showing that if an integer-valued random variable $W$ satisfies a certain negative dependence assumption, then $W$ is smaller (in the convex sense) than a Poisson variable of equal…
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the…
A characterization of the exponential distribution based on equidistribution conditions for maxima of random samples with consecutive sizes n-1 and n for an arbitrary and fixed n>2 is proved. This solves an open problem stated recently in…
Let $X$ and $Y$ be two real-valued random variables. Let $(X_{1},Y_{1}),(X_{2},Y_{2}),\ldots$ be independent identically distributed copies of $(X,Y)$. Suppose there are two players A and B. Player A has access to $X_{1},X_{2},\ldots$ and…
Let (X_n,Y_n), n\ge 1 be bivariate random claim sizes with common distribution function F and let N(t), t \ge 0 be a stochastic process which counts the number of claims that occur in the time interval [0,t], t\ge 0. In this paper we derive…
There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a…
Let $X_1,X_2,\ldots$ and $Y_1,Y_2,\ldots$ be two random sequences so that every random variable takes values in a finite set $\mathbb{A}$. We consider a global similarity score $L_n:=L(X_1,\ldots,X_n;Y_1,\ldots,Y_n)$ that measures the…
It is well known that the ratio of two independent standard Gaussian random variables follows a Cauchy distribution. Any convex combination of independent standard Cauchy random variables also follows a Cauchy distribution. In a recent…
A new family of continuous distribution is proposed by using Kumaraswamy-G (Cordeiro and de Castro, 2011) distribution as the base line distribution in the Marshal-Olkin (Marshall and Olkin, 1997) construction. A number of known…
In this work, we establish some stochastic comparison results for multivariate skew-elliptical random vectors. These multivariate stochastic comparisons involve Hessian and increasing-Hessian orderings as well as many of their special…