• Thumbnail for Independent and identically distributed random variables
    theory and statistics, a collection of random variables is independent and identically distributed (i.i.d., iid, or IID) if each random variable has the...
    14 KB (2,119 words) - 03:46, 30 June 2025
  • to the use of independent and identically distributed random variables in statistical models. Exchangeable sequences of random variables arise in cases...
    17 KB (2,561 words) - 20:51, 5 March 2025
  • Thumbnail for Gamma distribution
    parameterization, both offering insights into the behavior of gamma-distributed random variables. The gamma distribution is integral to modeling a range of phenomena...
    66 KB (9,100 words) - 06:11, 7 July 2025
  • Thumbnail for White noise
    White noise (redirect from Random shock)
    samples be independent and have identical probability distribution (in other words independent and identically distributed random variables are the simplest...
    30 KB (4,037 words) - 08:39, 28 June 2025
  • Thumbnail for Standard error
    Standard error (category Statistical deviation and dispersion)
    be derived from the variance of a sum of independent random variables, given the definition of variance and some properties thereof. If x 1 , x 2 , …...
    20 KB (2,781 words) - 01:28, 24 June 2025
  • Thumbnail for Independence (probability theory)
    (statistics) Independent and identically distributed random variables Mean dependence Normally distributed and uncorrelated does not imply independent Russell...
    28 KB (4,646 words) - 18:07, 22 June 2025
  • real-valued, independent and identically distributed random variables and let N ≥ 0 be an integer-valued random variable that is independent of the sequence...
    25 KB (3,188 words) - 01:42, 27 April 2024
  • of properly normalized maxima of a sequence of independent and identically distributed random variables. Note that a limit distribution needs to exist...
    26 KB (3,823 words) - 21:58, 3 April 2025
  • Thumbnail for Erlang distribution
    {\displaystyle X,Y} are independent The Erlang distribution is the distribution of the sum of k independent and identically distributed random variables, each having...
    15 KB (1,969 words) - 20:24, 19 June 2025
  • Thumbnail for Exponential distribution
    Peter J. (2016). "Entropy of the sum of two independent, non-identically-distributed exponential random variables". arXiv:1609.02911 [cs.IT]. Leemis, Lawrence...
    43 KB (6,647 words) - 17:34, 15 April 2025
  • Thumbnail for Normal distribution
    \ldots ,X_{n}} are independent and identically distributed random variables with the same arbitrary distribution, zero mean, and variance σ 2 {\textstyle...
    148 KB (21,531 words) - 03:40, 1 July 2025
  • Thumbnail for Log-normal distribution
    distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln X has...
    90 KB (12,551 words) - 22:45, 22 May 2025
  • Circular law (category Algebra of random variables)
    random n × n matrices whose entries are independent and identically distributed random variables, all with mean zero and variance equal to 1/n, the limiting...
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  • theorem (CLT) states that, in many situations, when independent and identically distributed random variables are added, their properly normalized sum tends...
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  • result of a tossed coin Independent and identically distributed random variables, statistically independent and having the same probability distribution...
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  • 1\,\}} are independent and identically distributed random variables, with distribution function G, which are also independent of { N ( t ) : t ≥ 0 } . {\displaystyle...
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  • a breathalyzer connected to a vehicle's engine Independent and identically distributed random variables in probability theory Interaural intensity difference...
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  • Thumbnail for Poisson distribution
    the sequence of inter-arrival times are independent and identically distributed exponential random variables having mean 1/λ.: 317–319  The cumulative...
    81 KB (11,215 words) - 08:39, 14 May 2025
  • Thumbnail for Geometric distribution
    exist n {\displaystyle n} independent identically distributed random variables whose sum is also geometrically distributed. This is because the negative...
    35 KB (5,094 words) - 06:38, 7 July 2025
  • Thumbnail for Random walk
    characterized by the steps being defined by independent and identically distributed random variables. Random walks can take place on a variety of spaces...
    56 KB (7,703 words) - 20:27, 29 May 2025
  • Thumbnail for Central limit theorem
    of independent, identically distributed random variables is a mixing random process in discrete time; "mixing" means, roughly, that random variables temporally...
    67 KB (9,202 words) - 03:48, 9 June 2025
  • (1)} That is: given a sequence of independent and identically distributed random variables, each having mean zero and positive variance, if additionally...
    18 KB (2,643 words) - 11:58, 1 May 2025
  • Kirkwood approximation Independent identically-distributed random variables Independent and identically-distributed random variables Statistical independence...
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  • Thumbnail for Random variable
    of checking equality of certain functions of independent, identically distributed (IID) random variables. However, the moment generating function exists...
    42 KB (6,634 words) - 15:00, 24 May 2025
  • Thumbnail for Probability theory
    {1}{n}}{\sum _{k=1}^{n}X_{k}}} of a sequence of independent and identically distributed random variables X k {\displaystyle X_{k}} converges towards their...
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  • statistics, a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF is...
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  • Thumbnail for Law of large numbers
    distributed (i.i.d.) random variables on [0, 1]. Then let Xi = a + (b - a) Ui for i= 1, 2, …, n. Then X1, X2, …, Xn are independent and identically distributed...
    45 KB (6,394 words) - 13:13, 25 June 2025
  • possible data compression for data whose source is an independent identically-distributed random variable, and the operational meaning of the Shannon entropy...
    12 KB (1,881 words) - 21:05, 11 May 2025
  • Thumbnail for Stochastic process
    process, which is a sequence of independent and identically distributed (iid) random variables, where each random variable takes either the value one or...
    168 KB (18,657 words) - 11:11, 30 June 2025
  • stochastic processes, such as random graphs. Suppose that a problem involves independent and identically-distributed random variables and that estimation of a...
    10 KB (1,553 words) - 11:19, 19 November 2024