Sentence examples for marginal distribution function from inspiring English sources

A practical framework for generating cross correlated random fields with a specified marginal distribution function, an autocorrelation function and cross correlation coefficients is presented in the paper.

In the univariate analysis, it is shown that a 3-component Lognormal mixture model provides a good fit to the marginal distribution function of fixation duration, and a hierarchical model is required for modeling saccade length.

Random variables (r.v.s) are not assumed to be mutually independent; it is assumed, however, that they have a common unknown continuous marginal distribution function (d.f).f

Lemma 2.2 Let {X n }n≥1be a second-order stationary NA sequence with common marginal distribution function and EX n = 0, |X n | ≤ d< ∞, n = 1,2,...

Theorem 1.1 Let 0 < p < 1 and { X n } n ≥ 1 be a second-order stationary NA sequence with common marginal distribution function F and E X n = 0 for n = 1, 2, …  .

Assume that {X n }n≥1is a sequence of random variables defined on a fixed probability space ( Ω, F, P ) with a common marginal distribution function F x) = P X1 ≤ x).

This method requires a priori information such as variables' marginal distribution functions and their correlation matrix.

Moreover, the continuity of the marginal distribution functions is not required so that data with ties and, particularly, ordered categorical data are covered by this model.

That is, even under the null hypothesis, the marginal distribution functions in the different groups may have different shapes, and are not assumed to be equal.

Comparing whether the marginal distribution functions of a k-dimensional random variable are equal or not is a classical problem in statistical inference.

Sklar theorem presents an n-dimension function which can be decomposed into n number marginal distribution functions and a Copula function.