|
Inversion Sampling
Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, or the Smirnov transform) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given its cumulative distribution function. Inverse transformation sampling takes uniform samples of a number u between 0 and 1, interpreted as a probability, and then returns the smallest number x\in\mathbb R such that F(x)\ge u for the cumulative distribution function F of a random variable. For example, imagine that F is the standard normal distribution with mean zero and standard deviation one. The table below shows samples taken from the uniform distribution and their representation on the standard normal distribution. We are randomly choosing a proportion of the area under the curve and returning the number in the domain such that exactly this proportion of the area occurs t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikolai Smirnov (mathematician)
Nikolai Vasilyevich Smirnov (; 17 October 1900 – 2 June 1966) was a Soviet Russian mathematician noted for his work in various fields including probability theory and statistics. Smirnov's principal works in mathematical statistics and probability theory were devoted to the investigation of limit distributions by means of the asymptotic behaviour of multiple integrals as the multiplicity is increased with limit. He was one of the creators of the nonparametric methods in mathematical statistics and of the theory of limit distributions of order statistics. Biography Smirnov was born October 17, 1900, in Moscow into the family of a church clerk who was also employed as a clerk in the office of the Bolshoi Theater. He completed his gymnasium education during the First World War, during which he served in various medical units of the military. After the October Revolution Smirnov joined the ranks of the Red Army. During this time he took an interest in philosophy and philology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
