Ad
related to: what does positive divergence mean in statistics examples list of symbols
Search results
Results From The WOW.Com Content Network
The only divergence for probabilities over a finite alphabet that is both an f-divergence and a Bregman divergence is the Kullback–Leibler divergence. [8] The squared Euclidean divergence is a Bregman divergence (corresponding to the function x 2 {\displaystyle x^{2}} ) but not an f -divergence.
¯ = sample mean of differences d 0 {\displaystyle d_{0}} = hypothesized population mean difference s d {\displaystyle s_{d}} = standard deviation of differences
Random variables are usually written in upper case Roman letters, such as or and so on. Random variables, in this context, usually refer to something in words, such as "the height of a subject" for a continuous variable, or "the number of cars in the school car park" for a discrete variable, or "the colour of the next bicycle" for a categorical variable.
This does not look random, but it satisfies the definition of random variable. This is useful because it puts deterministic variables and random variables in the same formalism. The discrete uniform distribution, where all elements of a finite set are equally likely. This is the theoretical distribution model for a balanced coin, an unbiased ...
Jensen–Shannon divergence; Bhattacharyya distance (despite its name it is not a distance, as it violates the triangle inequality) f-divergence: generalizes several distances and divergences; Discriminability index, specifically the Bayes discriminability index, is a positive-definite symmetric measure of the overlap of two distributions.
As an example, consider air as it is heated or cooled. The velocity of the air at each point defines a vector field. While air is heated in a region, it expands in all directions, and thus the velocity field points outward from that region. The divergence of the velocity field in that region would thus have a positive value.
The term "divergence" is in contrast to a distance (metric), since the symmetrized divergence does not satisfy the triangle inequality. [10] Numerous references to earlier uses of the symmetrized divergence and to other statistical distances are given in Kullback (1959, pp. 6–7, §1.3 Divergence).
When X n converges in r-th mean to X for r = 2, we say that X n converges in mean square (or in quadratic mean) to X. Convergence in the r-th mean, for r ≥ 1, implies convergence in probability (by Markov's inequality). Furthermore, if r > s ≥ 1, convergence in r-th mean implies convergence in s-th mean. Hence, convergence in mean square ...