Examples of "variates"
where "N" is the total number of variates of type "X" in the study, "K" is the number of samples in the study and "x" and "p" are the number of variates and the proportion of variates of type "X" respectively in the "i" sample.
where "X" is the sum of the "N" "x" variates and the "x" are the "n" members of the sample. Then the ratio of the sum of the "y" variates and the sum of the "x" variates chosen in this fashion is an unbiased estimate of the ratio estimator.
where "s" and "s" are the variances of the "x" and "y" variates respectively, "m" and "m" are the means of the "x" and "y" variates respectively and "s" is the covariance of "a" and "b".
where "m" is the mean of the "x" variate, "s" and "s" are the sample variances of the "x" and "y" variates respectively and "ρ" is the sample correlation between the "x" and "y" variates.
Also, the "k"th order statistic of "n" uniformly distributed variates is formula_346, so an alternative if α and β are small integers is to generate α + β − 1 uniform variates and choose the α-th smallest.
For normally distributed "x" and "y" variates the skewness of the ratio is approximately
Other methods for generating exponential variates are discussed by Knuth and Devroye.
The use of the antithetic variates method to estimate the result shows an important variance reduction.
where "p" is the proportion of the sample made up of variates of type "X" and
For the generation of non-uniform random variates, see Pseudo-random number sampling.
In the mathematical fields of probability and statistics, a random variate is a particular outcome of a random variable: the random variates which are other outcomes of the same random variable might have different values. Random variates are used when simulating processes driven by random influences (stochastic processes). In modern applications, such simulations would derive random variates corresponding to any given probability distribution from computer procedures designed to create random variates corresponding to a uniform distribution, where these procedures would actually provide values chosen from a uniform distribution of pseudorandom numbers.
The variance was significantly reduced after using the control variates technique. (The exact result is formula_29.)
For the generation of uniform random variates, see Random number generation.
A fast method for generating a set of ready-ordered exponential variates without using a sorting routine is also available.
To simplify the notation "s" will be used subsequently to denote the covariance between the variates "a" and "b".
where "n" is the sample size, "N" is the population size, "m" is the mean of the variate "x", "s" and "s" are the sample variances of the "x" and "y" variates respectively and "ρ" is the sample correlation between the "x" and "y" variates.
In statistics, the antithetic variates method is a variance reduction technique used in Monte Carlo methods. Considering that the error reduction in the simulated signal (using Monte Carlo methods) has a square root convergence, a very large number of sample paths is required to obtain an accurate result. The antithetic variates method reduces the variance of the simulation results.
where "n" is the size of the sample and the "r" are estimated with the omission of one pair of variates at a time.
Temugin had been named after his, and the Mandarin's, claimed ancestor Genghis Khan, whose birth name was Temujin (also spelled Temuchin, Temudjin, u also variates to ü).
A random variate of the "F"-distribution with parameters "d" and "d" arises as the ratio of two appropriately scaled chi-squared variates: