A test that relies on different assumptions is Fisher's exact test; if its assumption of fixed marginal distributions is met it is substantially more accurate in obtaining a significance level, especially with few observations.
42.
The argument is sometimes expressed in an alternative way by having the posterior marginal distribution of " n " based on " N " without explicitly invoking a non-zero chance of existing.
43.
The D4? width, unlike the FWHM and 1 / e 2 widths, is meaningful for multimodal marginal distributions that is, beam profiles with multiple peaks but requires careful subtraction of the baseline for accurate results.
44.
Factor graphs can be combined with message passing algorithms to efficiently compute certain characteristics of the function g ( X _ 1, X _ 2, \ dots, X _ n ), such as the marginal distributions.
45.
\boldsymbol \ Sigma _ { XX } and \ boldsymbol \ Sigma _ { YY } can be identified as the variance matrices of the marginal distributions for \ boldsymbol { X } and \ boldsymbol { Y } respectively.
46.
Measurements of the 1 / e 2 width only depend on three points on the marginal distribution, unlike D4? and knife-edge widths that depend on the integral of the marginal distribution . 1 / e 2 width measurements are noisier than D4? width measurements.
47.
Measurements of the 1 / e 2 width only depend on three points on the marginal distribution, unlike D4? and knife-edge widths that depend on the integral of the marginal distribution . 1 / e 2 width measurements are noisier than D4? width measurements.
48.
The distribution of the marginal variables ( the marginal distribution ) is obtained by "'marginalizing "'over the distribution of the variables being discarded, and the discarded variables are said to have been "'marginalized out " '.
49.
Given two random variables " X " and " Y " whose joint distribution is known, the marginal distribution of " X " is simply the probability distribution of " X " averaging over information about " Y ".
50.
The copula " C " contains all information on the dependence structure between the components of ( X _ 1, X _ 2, \ dots, X _ d ) whereas the marginal cumulative distribution functions F _ i contain all information on the marginal distributions.
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