Examples of "variate"
where formula_39 is standard normal random variate. The exponential random variate is :
Given a random variate "U" drawn from the uniform distribution in the interval (0, 1), then the variate
Given a random variate "U" drawn from the uniform distribution in the interval (0, 1), then the variate
If X is a random variate drawn from an asymmetric Laplace distribution (ALD), then formula_16 will be a circular variate drawn from the wrapped ALD, and, formula_17 will be an angular variate drawn from the wrapped ALD with formula_18.
where R(0,1) is the uniform random variate in the interval [0,1]. Using these two, we can derive the random variate for the MLP distribution to be:
the variate formula_26 has a Gumbel distribution with parameters formula_27 and formula_28 when the random variate formula_29 is drawn from the uniform distribution on the interval formula_30.
The estimated total of the "y" variate ( "τ" ) is
or, alternatively, for a random variate formula_27 for which
If "X" is a random variate drawn from a linear probability distribution "P", then formula_53 will be a circular variate distributed according to the wrapped "P" distribution, and formula_54 will be the angular variate distributed according to the wrapped "P" distribution, with formula_55.
Random samples from the Lévy distribution can be generated using inverse transform sampling. Given a random variate "U" drawn from the uniform distribution on the unit interval (0, 1], the variate "X" given by
So one algorithm for generating beta variates is to generate "X"/("X" + "Y"), where "X" is a gamma variate with parameters (α, 1) and "Y" is an independent gamma variate with parameters (β, 1).
A conceptually very simple method for generating exponential variates is based on inverse transform sampling: Given a random variate "U" drawn from the uniform distribution on the unit interval (0, 1), the variate
Multi-variate information and conditional multi-variate information can be decomposed into a sum of entropies, by Jakulin & Bratko (2003). The general expression for interaction information on variable set formula_9 in terms of the marginal entropies:
Random samples can be generated using inverse transform sampling. Given a random variate "U" drawn from the uniform distribution on the unit interval (0, 1], the variate "T" given by
Let formula_4 denote a "p"-variate normal distribution with location formula_5 and known covariance formula_6. Let
The mode of a variate "X" distributed as formula_12 is formula_13.
Generate another random variate, this time sampled from a uniform distribution between 0 and 1
The Cauchy distribution is the maximum entropy probability distribution for a random variate formula_27 for which
With the variate "L" we define a probability formula_8 that satisfies
The ratio estimate of a value of the "y" variate ("θ") is