More generally, the application of a given nonlinear transformation to a discrete distribution of points, computed so as to capture a set of known statistics of an unknown distribution, is referred to as an " unscented transformation ".
32.
Note that the formulae here reduce to the case of a finite or infinite mixture if the density " w " is allowed to be a generalized function representing the " derivative " of the cumulative distribution function of a discrete distribution.
33.
In computer science, for example, the metric " W " 1 is widely used to compare discrete distributions, " e . g . " the color histograms of two digital images; see earth mover's distance for more details.
34.
This says that the expected probability of seeing a category " i " among the various discrete distributions generated by the posterior distribution is simply equal to the proportion of occurrences of that category actually seen in the data, including the pseudocounts in the prior distribution.
35.
In a discrete distribution the characteristic function of any real-valued random variable is defined as the expected value of e ^ { itX }, where " i " is the imaginary unit and " t " & isin; " R"
36.
"The Art of Computer Programming " ?.4 . 1 . A ( vol . 2 pp 120-121 in the third edition ) shows a clever way to generate a random number from an arbitrary discrete distribution, with one call to the random number generator.
37.
Instead of imagining that each data point is first assigned a cluster and then drawn from the distribution associated to that cluster we now think of each observation being associated with parameter \ tilde { \ mu } _ { i } drawn from some discrete distribution G with support on the K means.
38.
:: For example : " The objective of this work is to present a rigorous formalism for the solution of engineering problems on vibrations in which the vibrating structure has a discrete distribution of loads . " But there are plenty of mathematical or technical texts setting their objective to outline / present / develop a " rigorous formalism " for some problem / field / issue.
39.
The probabilistic convolution tree-based dynamic programming method also efficiently solves the probabilistic generalization of the change-making problem, where uncertainty or fuzziness in the goal amount " W " makes it a discrete distribution rather than a fixed quantity, where the value of each coin is likewise permitted to be fuzzy ( for instance, when an exchange rate is considered ), and where different coins may be used with particular frequencies.
40.
:It's equivalent ( for non-discrete distributions ) to saying that z = f ( x ) with f ( x ) \ ge x, although only in the sense that " z " has that distribution, not that it is dependent on " x " . ( We are talking only about independent variables here, right ? ) So you could say that it is an " improvement " on " x " in that it replaces each value of " x " with one that is no smaller.
