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...

to the use of independent and identically distributed random variables in statistical models. Exchangeable sequences of random variables arise in cases...

parameterization, both offering insights into the behavior of gamma-distributed random variables. The gamma distribution is integral to modeling a range of phenomena...

the sequence of inter-arrival times are independent and identically distributed exponential random variables having mean 1/λ.: 317–319  The cumulative...

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 , …...

samples be independent and have identical probability distribution (in other words independent and identically distributed random variables are the simplest...

of properly normalized maxima of a sequence of independent and identically distributed random variables. Note that a limit distribution needs to exist...

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...

{\displaystyle X,Y} are independent The Erlang distribution is the distribution of the sum of k independent and identically distributed random variables, each having...

real-valued, independent and identically distributed random variables and let N ≥ 0 be an integer-valued random variable that is independent of the sequence...

(statistics) Independent and identically distributed random variables Mean dependence Normally distributed and uncorrelated does not imply independent Russell...

theorem (CLT) states that, in many situations, when independent and identically distributed random variables are added, their properly normalized sum tends...

Peter J. (2016). "Entropy of the sum of two independent, non-identically-distributed exponential random variables". arXiv:1609.02911 [cs.IT]. Leemis, Lawrence...

of independent, identically distributed random variables is a mixing random process in discrete time; "mixing" means, roughly, that random variables temporally...

\ldots ,X_{n}} are independent and identically distributed random variables with the same arbitrary distribution, zero mean, and variance σ 2 {\textstyle...

1\,\}} are independent and identically distributed random variables, with distribution function G, which are also independent of { N ( t ) : t ≥ 0 } . {\displaystyle...

result of a tossed coin Independent and identically distributed random variables, statistically independent and having the same probability distribution...

(1)} That is: given a sequence of independent and identically distributed random variables, each having mean zero and positive variance, if additionally...

Kirkwood approximation Independent identically-distributed random variables Independent and identically-distributed random variables Statistical independence...

exist n {\displaystyle n} independent identically distributed random variables whose sum is also geometrically distributed. This is because the negative...

characterized by the steps being defined by independent and identically distributed random variables. Random walks can take place on a variety of spaces...

distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified/constant/fixed number...

{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...

a breathalyzer connected to a vehicle's engine Independent and identically distributed random variables in probability theory Interaural intensity difference...

of checking equality of certain functions of independent, identically distributed (IID) random variables. However, the moment generating function exists...

identically 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...

density, ƒn is its estimate based on a sample of n independent and identically distributed random variables. Here, E denotes the expected value with respect...

statistics, a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF is...

independent, identically distributed (i.i.d.) random variables, all Bernoulli trials with success probability p, then their sum is distributed according...

stochastic processes, such as random graphs. Suppose that a problem involves independent and identically-distributed random variables and that estimation of a...