Elasticity is a very popular concept in economics and physics, recently exported and reinterpreted in the statistical field, where it has given form to the so-called elasticity function. This function has proved to be a very useful tool for quantifying and evaluating risks, with applications in...

We provide a simple identity that decomposes a product moment of multivariate normal random variables as a sum of various products of univariate moments of one of the random variables and multivariate moments of the other random variables. The new identity allows for much faster computation of...

The random utility model (RUM, McFadden and Richter (1990)) has been the standard tool to describe the behavior of a population of decision makers. RUM assumes that decision makers behave as if they maximize a rational preference over a choice set. This assumption may fail when consideration of...

Elasticity is a very popular concept in economics and physics, recently exported and reinterpreted in the statistical field, where it has given form to the so-called elasticity function. This function has proved to be a very useful tool for quantifying and evaluating risks, with applications in...

There has been much work on the approximation of independent or dependent random variables. But we are not aware of any work giving exact results for the approximation of the sum of randomly weighted random variables. In this paper, we derive results for the randomly weighted sum of dependent...

Feature selection becomes a prominent method in the big data era. The logistic regression model is a wrapper method that provides better classification or prediction accuracy but it is computationally expensive. In this study, we propose the random subspace logistic regression where features are...

This paper studies random vectors X featuring symmetric distributions in that i) the order of the random variables in X does not affect its distribution, or ii) the distribution of X is symmetric at zero. We derive a number of characterization results for such random vectors, thereby connecting...

We introduce the new F-Riesz distribution to model tail-heterogeneity in fat-tailed covariance matrix observations. In contrast to the typical matrix-valued distributions from the econometric literature, the F-Riesz distribution allows for different tail behavior across all variables in the...

As simulation arid Monte Carlo continue to play an increasing role in statistical research, careful attention must be given to problems which arise in implementing and documenting collect ions of random number generators. This paper examines the value of theoretical as well as empirical evidence...

We design a laboratory experiment to identify whether a preference for randomization defines a stable type across different choice environments. In games and individual decisions, subjects face twenty simultaneous repetitions of the same choice. Subjects can randomize by making different choices...

The Markov inequality is a classical nice result in statistics that serves to demonstrate other important results as the Chebyshev inequality and the weak law of large numbers, and that has useful applications in the real world, when the random variable is unspecified, to know an upper bound for...

This paper considers the randomly weighted sums generated by some dependent sub-exponential primary random variables and some arbitrarily dependent random weights. To study the randomly weighted sums with infinitely many terms, we establish a Kesten-type upper bound for their tail probabilities...

The problem of determining distributions of the product of random variables is one of the most important problems. However, most studies only focus on independence structures on some common distributions of the functions of random variables or stochastic dependence through multivariate normal...

Determining distributions of the functions of random variables is a very important problem with wide applications in Risk Management, Finance, Economics, Science, and many other areas. This paper develops the theory on both density and distribution functions for the quotient Y = X₁/X ₂ and the...

Determining distributions of the functions of random variables is one of the most important problems in statistics and applied mathematics because distributions of functions have wide range of applications in numerous areas in economics, finance, risk management, science, and others. However,...

Determining distributions of the functions of random variables is a very important problem with a wide range of applications in Risk Management, Finance, Economics, Science, and many other areas. This paper develops the theory on both density and distribution functions for the quotient Y=X1X2...

In this paper, we establish some results on strong convergence for sums and weighted sums of uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in

It is already known, under certain conditions including stochastic inequalities, the comparison of moments. In this paper, we will study in detail the reverse of this problem, that is, the stochastic orderings implied by moments inequalities. We will limit our study to the absolute value of...

The exact distribution of a linear combination with positive coefficients of inverted chi-square variables with odd degrees of freedom is derived. This distribution function could be expressed as another linear combination of distribution functions of chi-square random variables

Let , ,…, be a sequence of independent random variables, let be a rearrangement invariant space on the underlying probability space, and let be a symmetric sequence space. This paper gives an approximate formula for the quantity whenever embeds into for some 1 ≤ ∞. This extends work of...

We consider possible measures of dependence for two symmetric alpha-stable (SαS) random variables. Some results are given which enlighten a few deficiencies of these measures. We propose a new measure which partially solve these problems. The results are illustrated by simulations

An exact algorithm for generating two positively correlated Beta-distributed random variables is provided. The paired Beta-distributed random variables are generated from ratios of independent standard Gamma distributions. A positive correlation is achieved by introducing two shared standard...

The Lerch family of three-parameter, discrete univariate distributions includes as special cases the well known Zipf, Zipf-Mandelbrot, and Good distributions that are used as models in ecology, linguistics, information science, and statistical physics. The Lerch distribution was originally...

Linear Programming model is an important tool used to solve constrained optimization problems. In fact, the real life problems are usually occurring in the presence of uncertainty. For instance, in managerial problems of assigning employees to different tasks with the aim of minimizing the total...

Supplementary Appendix is available at: "https://ssrn.com/abstract=2970015" https://ssrn.com/abstract=2970015. Decision making in finance often requires an accurate estimate of the coskewness matrix to optimize the allocation to random variables with asymmetric distributions. The classical...

This paper proposes a decision-theoretic framework for experiment design. We model experimenters as ambiguity-averse decision-makers, who make trade-offs between subjective expected performance and robustness. This framework accounts for experimenters' preference for randomization, and clarifies...

This paper studies inference for the average treatment effect in randomized controlled trials with covariate-adaptive randomization. Here, by covariate-adaptive randomization, we mean randomization schemes that first stratify according to baseline covariates and then assign treatment status so...