In probability and statistics, a Bernoulli process (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is...

formalization and advanced formulation of the Bernoulli trial is known as the Bernoulli process. Since a Bernoulli trial has only two possible outcomes, it...

probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution...

reference to Bernoulli, by Ladislaus Bortkiewicz who in 1917 wrote in German the word stochastik with a sense meaning random. The term stochastic process first...

2024. Bernoulli differential equation Bernoulli distribution Bernoulli number Bernoulli polynomials Bernoulli process Bernoulli trial Bernoulli's principle...

Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. For example, for a fluid flowing horizontally Bernoulli's...

Bernoulli family of Basel. Bernoulli differential equation Bernoulli distribution Bernoulli number Bernoulli polynomials Bernoulli process Bernoulli Society...

Jacob Bernoulli (also known as James in English or Jacques in French; 6 January 1655 [O.S. 27 December 1654] – 16 August 1705) was a Swiss mathematician...

two methods of observation of some random process. Consider observing the first n trials of a Bernoulli process, and seeing that A of them are successes...

mathematics, the Bernoulli scheme or Bernoulli shift is a generalization of the Bernoulli process to more than two possible outcomes. Bernoulli schemes appear...

independent of the past states). A Bernoulli scheme with only two possible states is known as a Bernoulli process. Note, however, by the Ornstein isomorphism...

his father Johann Bernoulli and one of his brothers, Daniel Bernoulli. He was one of the many prominent mathematicians in the Bernoulli family. Nicolaus...

processes Basic affine jump diffusion Bernoulli process: discrete-time processes with two possible states. Bernoulli schemes: discrete-time processes...

transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation)...

stochastic process X {\displaystyle X} is an adapted process with respect to its natural filtration. Two examples are given below, the Bernoulli process and...

Bernoulli number Bernoulli polynomials Bernoulli process Bernoulli trial Lemniscate of Bernoulli Bernoulli, a journal published by the Bernoulli Society for...

experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e....

of failures in a sequence of independent and identically distributed Bernoulli trials before a specified/constant/fixed number of successes r {\displaystyle...

population sampling, Bernoulli sampling is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines...

statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in...

pseudorandom number generator, but one may also use some external physical process, such as the last digits of the time given by the computer clock. A pseudorandom...

of coin flipping is described by means of the Bernoulli process; a single flip of a coin is a Bernoulli trial. In the study of statistics, coin-flipping...

interpreted as the Bernoulli process. One may generalize this to include continuous time Lévy processes, and many Lévy processes can be seen as limits...

\operatorname {H} _{\text{b}}(p)} , is defined as the entropy of a Bernoulli process (i.i.d. binary variable) with probability p {\displaystyle p} of one...

average process. The Ornstein isomorphism theorem states that every stationary stochastic process is equivalent to a Bernoulli scheme (a Bernoulli process with...

(1657) gave the earliest known scientific treatment of the subject. Jakob Bernoulli's Ars Conjectandi (posthumous, 1713) and Abraham de Moivre's Doctrine of...

= 0 ) = α {\displaystyle P(t=0)=\alpha } . Continuous-time stochastic process Continuous function Continuous geometry Continuous modelling Continuous...

statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it can be used to describe...

theory. Some fundamental discrete distributions are the discrete uniform, Bernoulli, binomial, negative binomial, Poisson and geometric distributions. Important...

Random variable Bernoulli process Continuous or discrete Expected value Variance Markov chain Observed value Random walk Stochastic process Complementary...