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This is useful because it puts deterministic variables and random variables in the same formalism. The discrete uniform distribution, where all elements of a finite set are equally likely. This is the theoretical distribution model for a balanced coin, an unbiased die, a casino roulette, or the first card of a well-shuffled deck.
The main idea is to introduce a new non-negative variable to the program which will be used to rescale the constants involved in the program (,,). This allows us to require that the denominator of the objective function ( d T x + β {\displaystyle \mathbf {d} ^{T}\mathbf {x} +\beta } ) equals 1.
A VAR with p lags can always be equivalently rewritten as a VAR with only one lag by appropriately redefining the dependent variable. The transformation amounts to stacking the lags of the VAR(p) variable in the new VAR(1) dependent variable and appending identities to complete the precise number of equations. For example, the VAR(2) model
The distribution of a random variable that is defined as the minimum of several random variables, each having a different Weibull distribution, is a poly-Weibull distribution. The Weibull distribution was first applied by Rosin & Rammler (1933) to describe particle size distributions.
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Markov's inequality (and other similar inequalities) relate probabilities to expectations, and provide (frequently loose but still useful) bounds for the cumulative distribution function of a random variable. Markov's inequality can also be used to upper bound the expectation of a non-negative random variable in terms of its distribution function.
Vector autoregressions are flexible statistical models that typically include many free parameters. Given the limited length of standard macroeconomic datasets relative to the vast number of parameters available, Bayesian methods have become an increasingly popular way of dealing with the problem of over-parameterization .
The variance of randomly generated points within a unit square can be reduced through a stratification process. In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computational effort. [1]