Dependent random variables and hypothesis testing—a Monte Carlo perspective

Monte Carlo Simulation of Correlated Random Variables

This paper describes a method for the Monte Carlo simulation of two correlated random variables. The author analyses linear combinations of stochastically independent random variables that are equally distributed over the interval (0; 1) (\random numbers") and also examines their distribution. If a suitable matrix of coeecients is chosen, the subsequent transformation results in random variable...

Imprecise random variables, random sets, and Monte Carlo simulation

The paper addresses the evaluation of upper and lower probabilities induced by functions of an imprecise random variable. Given a function g and a family Xλ of random variables, where the parameter λ ranges in an index set Λ, one may ask for the upper/lower probability that g(Xλ ) belongs to some Borel set B. Two interpretations are investigated. In the first case, the upper probability is comp...

Simulations of Continuous Random Variables and Monte Carlo Methods

In this paper we describe algorithms for computer simulations of some common continuous distributions and their implementation in MATLAB. We use Monte Carlo methods for estimating probabilities and other characteristics of random variables. The paper concludes with some interesting applications. AMS SUBJECT CLASSIFICATION: 60E05, 60G99, 60J10, 65C05, 65C60.

Guaranteed Monte Carlo Methods for Bernoulli Random Variables

Simple Monte Carlo is a versatile computational method with a convergence rate of O(n−1/2). It can be used to estimate the means of random variables whose distributions are unknown. Bernoulli random variables, Y , are widely used to model success (failure) of complex systems. Here Y = 1 denotes a success (failure), and p = E(Y ) denotes the probability of that success (failure). Another applica...

Central and Local Limit Theories in Markov Dependent Random Variables