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Topic: Independent and identically distributed

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	Independent and identically-distributed random variables - Wikipedia, the free encyclopedia
		In probability theory, a sequence or other collection of random variables is independent and identically distributed (i.i.d.) if each has the same probability distribution as the others and all are mutually independent.
		is particularly common in statistics (sometimes written IID), where observations in a sample are often assumed to be (more-or-less) i.i.d.
		All other things being equal, a sequence of outcomes of spins of a roulette wheel is i.i.d.
	en.wikipedia.org /wiki/Independent_identically-distributed_random_variables (228 words)

	De Finetti's theorem - Wikipedia, the free encyclopedia
		The condition of exchangeability is stronger than the assumption of identical distribution of the individual random variables in the sequence, and weaker than the assumption that they are independent and identically distributed.
		De Finetti's theorem states that the probability distribution of any infinite exchangeable sequence of Bernoulli random variables is a "mixture" of the probability distributions of independent and identically distributed sequences of Bernoulli random variables.
		The independence asserted here is conditional independence, i.e., the Bernoulli random variables in the sequence are conditionally independent given the event that p = 2/3, and are conditionally independent given the event that p = 9/10.
	en.wikipedia.org /wiki/De_Finetti's_theorem (562 words)

	Independent and identically distributed Monte Carlo algorithms for semiparametric linear mixed models. \| Journal of the ...
		Independent and identically distributed Monte Carlo algorithms for semiparametric linear mixed models.
		This article introduces a new class of independent and identically distributed (iid) Monte Carlo algorithms which can be used for inference in semiparametric linear mixed models under minimal assumptions for the random-effects distribution.
		In group 2, random slopes [[alpha].sub.i, 1] were simulated from a skewed distribution with mean chosen to coincide with the fixed-effects slope [[beta].sub.1] of group 1, whereas random intercepts [[alpha].sub.i, 0] were drawn from a discrete two-point mixture distribution.
	www.accessmylibrary.com /coms2/summary_0286-10047437_ITM (1549 words)

	Independent identically-distributed random variables - the free encyclopedia (Site not responding. Last check: 2007-10-31)
		sequence or other collection of random variables is independent and identically distributed (i.i.d.) if each has the same
		probability distribution as the others and all are mutually
		sample are typically assumed to be (more-or-less) i.i.d.
	www.encyclopedia-of-world-knowledge.com /default.asp?t=Independent_identically-distributed_random_variables (171 words)

	PlanetMath: independent identically distributed
		all have the same distribution, and are independent of each other, then we say that the
		Cross-references: mean, exponential distribution, Poisson process, independent, distribution, random variables, collection
		This is version 1 of independent identically distributed, born on 2004-07-01.
	planetmath.org /encyclopedia/IndependentIdenticallyDistributed.html (65 words)

	Sampling Theory - SAMPLING DISTRIBUTIONS - CENTRAL LIMIT THEOREM (Site not responding. Last check: 2007-10-31)
		The central limit theorem states that the sampling distribution of the mean, for any set of independent and identically distributed random variables, will tend towards the normal distribution as the sample size gets larger.
		The central limit theorem is one of the most important theorems in the field of probability as well as statistical inference, as it justifies the use of the normal curve in a wide range of statistical applications, both theoretical and practical.
		The normal approximation to the binomial distribution is a special case of the central limit theorem, where the independent random variables are Bernoulli variables with parameter p.
	library.advanced.org /10030/8stsdclt.htm (188 words)

	Independent identically-distributed random variables roulette central limit theorem Examples statistics sequence random ... (Site not responding. Last check: 2007-10-31)
		Let be independent but not necessarily identically distributed random variables, where ~ (,).
		X n is a sequence of independent and identically distributed random variables, with common probability density function f, then.
		A random sample is a sequence of independent, identically distributed random variables.
	en.powerwissen.com /OQGb2oaDwPcoaLs8B3I0hA%3D%3D_Independent__identically_distributed.html (293 words)

	Central limit theorem
		Intuitively, they all express the fact that any sum of many independent identically distributed random variable s is approximately normally distributed.
		But, this limit is just the characteristic function of a standard normal distribution, N(0,1), and the central limit theorem follows from the Lévy continuity theorem, which confirms that the convergence of characteristic functions implies convergence in distribution.
		The density of the sum of two or more independent variables is the convolution of their densities (if these densities exist).
	www.nebulasearch.com /encyclopedia/article/Central_limit_theorem.html (843 words)

	independent identically-distributed random variables (Site not responding. Last check: 2007-10-31)
		A sequence or other collection of random variables is independent and identically distributed (i.i.d.) if each has the same probability distribution as any of the others and all are mutually independent.
		Subsamples of a set of symmetric, independent, identically distributed random variables which determine a set of typical values (NRL report) (NRL report)
		Bounds for the distribution function of a sum of independent, identically distributed random variables (Mimeograph series - Institute of Statistics) (Mimeograph series - Institute of Statistics)
	www.abacci.com /wikipedia/topic.aspx?cur_title=independent_identically-distributed_random_variables (151 words)

	[No title]
		For independent identically distributed magnetic fields and special Anderson models, we compute the density of states using a random walk expansion.
		Independent identically distributed magnetic fields lead to new Anderson type models for which a spectral analysis \cite{Carmona,Cycon,Pastur} has still to be done.
		This is equivalent to taking real-valued random variables $\alpha(n)$ with uniform distribution on $[0,1]$ and to form the independent identically distributed potential $V(n)= 2 \cos(2 \pi \alpha(n))$ which has an absolutely continuous law $4 (2 \pi)^{-1} \sqrt{1-x^2}$.
	www.ma.utexas.edu /mp_arc/papers/95-195 (6575 words)

	Method for generating a correlated sequence of variates with desired marginal distribution for testing a model of a ...
		This method, to be described in more detail subsequently, uses as inputs an independent identically distributed random number stream of uniform marginals and a pair of specified control parameters, and subjects such inputs to a modulo 1 autoregressive scheme that yields a sequence of correlated variates with a uniform marginal distribution.
		More specifically, a random number generator is used to produce a sequence of independent identically distributed variates from which one is chosen to serve as the initial variate or seed in a modulo one autoregressive operation.
		In particular, the innovation variate is constructed to have a desired probability distribution in an interval chosen appropriately to introduce the desired autocorrelation.
	www.freepatentsonline.com /5257364.html (8062 words)

	TESTS OF NEW BETTER THAN RENEWAL USED WITH RANDOMLY CENSORED SAMPLES
		The random censoring samples motivated in the following: Let be a sequence of life lengths of n independent identically distributed random variables with distribution function F, and be a sequence of independent and identically distributed random variables with distribution function G and distributed independently of.
		As this is the survival of an exponential distribution, we have it to be that corresponding to an NWRU.
		Consider F to be the scale mixture of the exponential distributions with the mixing distribution as exponential with mean 1.
	www.minshawi.com /D_Jamal/NBRU.htm (2850 words)

	Sampling Theory - SAMPLING DISTRIBUTIONS - SAMPLE MEAN AND VARIANCE (Site not responding. Last check: 2007-10-31)
		The sampling distribution of the mean is the probability distribution of the mean of a random sample.
		The sampling distribution of the mean has the same mean as the original population, but its variance is smaller than that of the original population by a factor of 1/n.
		The sampling distribution of the sample variance is the probability distribution of the sample variance of a random sample.
	library.advanced.org /10030/8sdsmav.htm (229 words)

	Bootstrap Fit
		The residuals from the fit follow a common distribution, usually assumed to be the normal distribution.
		Residual resampling assumes fixed X values and independent and identically distributed residuals (although the residuals are not assumed to be normally distributed).
		If the bootstrap methods produce substantially different results, this is an indication that the assumptions of fixed X and independent and identically distributed residuals may not be valid.
	www.itl.nist.gov /div898/software/dataplot/refman1/auxillar/bootfit.htm (864 words)

	distributed identically independent random variable (Site not responding. Last check: 2007-10-31)
		the baseline (12) average entry-level wage offered, [epsilon] is an independent identically distributed random variable with mean 0, and the explanatory variables are described in exhibit 1.
		Statistical process control by a simple control chart of a process variable, is based on the assumption that the process variable is an independent identically distributed random variable.
		July 2005 where the intervals or counts between successive samples are independent identically distributed random variable.
	www.variableearth.com /earth/distributed+identically+independent+random+variable (634 words)

	Independent identically-distributed random variables (Site not responding. Last check: 2007-10-31)
		Limit Distributions for Sums of Independent Random Vectors : Heavy Tails in Theory and Practice (Wiley Series in Probability and Statistics)
		On the minimum of independent geometrically distributed random variables (SuDoc NAS 1.26:194883)
		Uniform Limit Theorems for Sums of Independent Random Variables (Proceedings of the Steklov Institute of Mathematics, Vol 174)
	www.freeglossary.com /Independent,_identically_distributed_random_variables (277 words)

	extRemes web tutorial: Appendix
		Note, however, that the independence assumption, which virtually never occurs for weather and climate variables, can be relaxed (see Dependence Issues).
		Two methods are available for this: the first method is an exploratory technique carried out prior to model estimation and the second method is an assessment of the stability of parameter estimates based on the fitting of models across a range of different thresholds (Coles (2001) (b).
		The asymptotic distribution approximation of maximums and exceedances over a threshold assumes that data are independent and identically distributed (iid), but this is often not the case with real data.
	www.isse.ucar.edu /extremevalues/tutorial/Appendix.html (1177 words)

	No Title
		are independent and identically distributed random variables then the sequence of sample means,:
		This is a sort of approximate distribution calculation.
		are independent and identically distributed random variables with
	www.stat.sfu.ca /~lockhart/richard/450/99_3/lectures/13/web.html (916 words)

	TESTS OF RANDOMLY CENSORED SAMPLES FROM
		The randomly censored samples can be defined as: Let be a sequence of life lengths of n independent identically distributed random variables with distribution function F, and be a sequence of independent and identically distributed random variables with distribution function G and distributed independently of.
		The distribution of the statistics is not badly skewed.
		For the Wiebull distribution the dependence of the power estimates on the parameter value are less than those for the Gamma and Pareto distributions.
	www.minshawi.com /D_Jamal/NBRUE.htm (2671 words)

	A Large Deviation Principle for Dirichlet Posteriors
		Let Xk be a sequence of independent and identically distributed random variables taking values in a compact metric space Ω, and consider the problem of estimating the law of K1 in a Bayesian framework.
		A conjugate family of priors for non-parametric Bayesian inference is the Dirichlet process priors popularized by Ferguson.
		We prove that if the prior distribution is Dirichlet, then the sequence of posterior distributions satisfies a large deviation principle, and give an explicit expression for the predictive probability of ruin in the classical gambler's ruin problem.
	research.microsoft.com /research/pubs/view.aspx?type=Publication&id=766 (88 words)

	Independent and identically distributed - MLpedia (Site not responding. Last check: 2007-10-31)
		A set of random variables is independent and identically distributed (i.i.d.) if each has the same probability distribution as the others and all are mutually independent.
		is used where observations are often assumed to be (more-or-less) i.i.d.
		A sequence of outcomes of spins of a roulette wheel is i.i.d.
	www.mlpedia.org /index.php?title=Independent_and_identically_distributed (134 words)

	CLRC: Computer Learning Research Centre (Site not responding. Last check: 2007-10-31)
		It demonstrates mathematically the validity of the reliability claimed by conformal predictors when they are applied to independent and identically distributed data, and it confirms experimentally that the accuracy is sufficient for many practical problems.
		Later chapters of the monograph generalize these results from independent and identically distributed data to models called repetitive structures, which originate in the algorithmic theory of randomness and statistical physics.
		The approach is flexible enough to incorporate most existing methods of machine learning, including newer methods such as boosting and support vector machines and older methods such as nearest neighbours and the bootstrap.
	www.clrc.rhul.ac.uk /publications/covers/algorithmiclearning.shtml (268 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		Suppose there are n independent and identically distributed random variables, X
		Then, under an appropriate change of probability measure determined from Girsanov's formula, the random variables are distributed with a different mean but the same variance.
		Girsanov's theorem applies to Brownian motion (independent and normally distributed increments), and, in general, to solutions of multidimensional differential equations.
	www.amex.com /servlet/AmexFnDictionary?pageid=display&titleid=2998 (77 words)

	Society for Scientific Exploration \| Journal of Scientific Exploration \| Introductory Remarks on Large Deviation ... (Site not responding. Last check: 2007-10-31)
		Usually only the Shannon entropy of equilibrium distributions such as a canonical distribution is considered.
		Entropies are considered for arbitrary distributions or physical states, and they describe, e.g., "how fast" non-equilibrium distributions and states "die out" with increasing number of degrees of freedom or increasing number of particles.
		In the particular case of experiments with independent and identically distributed (i.i.d.) events, Shannon entropy can be shown to play its usual role (Sanov's theorem).
	www.scientificexploration.org /jse/abstracts/v13n4a4.php (222 words)

	Necessary and Sufficient Conditions for Weak Consistency of the Median of Independent but not Identically Distributed ... (Site not responding. Last check: 2007-10-31)
		Abstract: : Necessary and sufficient conditions for the weak consistency of the sample median of independent, but not identically distributed random variables are given and discussed.
		27 the distribution of the number of successes in independent t..
		1 the distribution of the number of successes in independent t..
	citeseer.ifi.unizh.ch /1434.html (380 words)

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