Random variate

In probability and statistics, a random variate or simply variate is a particular outcome of a random variable; the random variates which are other outcomes of the same random variable might have different values (random numbers). A random deviate or simply deviate is the difference of a random variate with respect to the distribution central location (e.g., mean), often divided by the standard deviation of the distribution (i.e., as a standard score). Random variates are used when simulating processes driven by random influences (stochastic processes). In modern applications, such simulations would derive random variates corresponding to any given probability distribution from computer procedures designed to create random variates corresponding to a uniform distribution, where these procedures would actually provide values chosen from a uniform distribution of pseudorandom numbers. Procedures to generate random variates corresponding to a given distribution are known as procedures for (uniform) random number generation or non-uniform pseudo-random variate generation. In probability theory, a random variable is a measurable function from a probability space to a measurable space of values that the variable can take on. In that context, those values are also known as random variates or random deviates, and this represents a wider meaning than just that associated with pseudorandom numbers. Devroye defines a random variate generation algorithm (for real numbers) as follows: Assume that Computers can manipulate real numbers. Computers have access to a source of random variates that are uniformly distributed on the closed interval [0,1]. Then a random variate generation algorithm is any program that halts almost surely and exits with a real number x. This x is called a random variate. (Both assumptions are violated in most real computers. Computers necessarily lack the ability to manipulate real numbers, typically using floating point representations instead.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (14)

Related courses (4)

Related lectures (20)

Poisson distribution

In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson ('pwɑːsɒn; pwasɔ̃). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.

Random variate

Continuous uniform distribution

In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, and which are the minimum and maximum values. The interval can either be closed (i.e. ) or open (i.e. ). Therefore, the distribution is often abbreviated where stands for uniform distribution.

MATH-232: Probability and statistics

A basic course in probability and statistics

MATH-414: Stochastic simulation

The student who follows this course will get acquainted with computational tools used to analyze systems with uncertainty arising in engineering, physics, chemistry, and economics. Focus will be on s

COM-309: Introduction to quantum information processing

Information is processed in physical devices. In the quantum regime the concept of classical bit is replaced by the quantum bit. We introduce quantum principles, and then quantum communications, key d

Principles of Quantum Mechanics COM-309: Introduction to quantum information processing

Covers the principles of quantum mechanics, including the Measurement Principle and Max Born Rule.

Simulation & Optimization: Poisson Process & Random Numbers MATH-600: Optimization and simulation

Explores simulation pitfalls, random numbers, discrete & continuous distributions, and Monte-Carlo integration.

Nonuniform Random Number Distributions: Examples and Methods PHYS-403: Computer simulation of physical systems I

Explores nonuniform random number distributions, examples, methods, and generation techniques.