Definitions for central limit theorem
cen·tral lim·it the·o·rem

WiktionaryRate this definition:0.0 / 0 votes

1. central limit theoremnoun

   The theorem that states that if the sum of independent identically distributed random variables has a finite variance, then it will be approximately normally distributed.

2. central limit theoremnoun

   Any of various similar theorems.

WikipediaRate this definition:0.0 / 0 votes

1. Central limit theorem

   In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern general form, this fundamental result in probability theory was precisely stated as late as 1920, thereby serving as a bridge between classical and modern probability theory. If X 1 , X 2 , … , X n , … {\textstyle X_{1},X_{2},\dots ,X_{n},\dots } are random samples drawn from a population with overall mean μ {\textstyle \mu } and finite variance σ 2 {\textstyle \sigma ^{2}} , and if X ¯ n {\textstyle {\bar {X}}_{n}} is the sample mean of the first n {\textstyle n} samples, then the limiting form of the distribution, Z = lim n → ∞ ( X ¯ n − μ σ X ¯ ) {\textstyle Z=\lim _{n\to \infty }{\left({\frac {{\bar {X}}_{n}-\mu }{\sigma _{\bar {X}}}}\right)}} , with σ X ¯ = σ / n {\displaystyle \sigma _{\bar {X}}=\sigma /{\sqrt {n}}} , is a standard normal distribution.For example, suppose that a sample is obtained containing many observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic mean of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the probability distribution of the average will closely approximate a normal distribution. The central limit theorem has several variants. In its common form, the random variables must be independent and identically distributed (i.i.d.). In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions or for non-independent observations, if they comply with certain conditions. The earliest version of this theorem, that the normal distribution may be used as an approximation to the binomial distribution, is the de Moivre–Laplace theorem.

WikidataRate this definition:0.0 / 0 votes

1. Central limit theorem

   In probability theory, the central limit theorem states that, given certain conditions, the mean of a sufficiently large number of independent random variables, each with a well-defined mean and well-defined variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common form, the random variables must be identically distributed. In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions, given that they comply with certain conditions. In more general probability theory, a central limit theorem is any of a set of weak-convergence theories. They all express the fact that a sum of many independent and identically distributed random variables, or alternatively, random variables with specific types of dependence, will tend to be distributed according to one of a small set of attractor distributions. When the variance of the i.i.d. variables is finite, the attractor distribution is the normal distribution. In contrast, the sum of a number of i.i.d. random variables with power law tail distributions decreasing as |x|−α−1 where 0 < α < 2 will tend to an alpha-stable distribution with stability parameter of α as the number of variables grows.

How to pronounce central limit theorem?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say central limit theorem in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of central limit theorem in Chaldean Numerology is: 5

2. Pythagorean Numerology

   The numerical value of central limit theorem in Pythagorean Numerology is: 4

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Central_Limit_Theorem
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Central_Limit_Theorem
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=central limit theorem