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The total variation distance (or half the norm) arises as the optimal transportation cost, when the cost function is (,) =, that is, ‖ ‖ = (,) = {(): =, =} = [], where the expectation is taken with respect to the probability measure on the space where (,) lives, and the infimum is taken over all such with marginals and , respectively.
Greek letters (e.g. θ, β) are commonly used to denote unknown parameters (population parameters). [3]A tilde (~) denotes "has the probability distribution of". Placing a hat, or caret (also known as a circumflex), over a true parameter denotes an estimator of it, e.g., ^ is an estimator for .
is known as Campbell's formula [2] or Campbell's theorem, [1] [12] [13] which gives a method for calculating expectations of sums of measurable functions with ranges on the real line. More specifically, for a point process N {\displaystyle N} and a measurable function f : R d → R {\displaystyle f:{\textbf {R}}^{d}\rightarrow {\textbf {R ...
Stein's method is a general method in probability theory to obtain bounds on the distance between two probability distributions with respect to a probability metric.It was introduced by Charles Stein, who first published it in 1972, [1] to obtain a bound between the distribution of a sum of -dependent sequence of random variables and a standard normal distribution in the Kolmogorov (uniform ...
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In statistics, Cohen's h, popularized by Jacob Cohen, is a measure of distance between two proportions or probabilities. Cohen's h has several related uses: It can be used to describe the difference between two proportions as "small", "medium", or "large". It can be used to determine if the difference between two proportions is "meaningful".
within a certain time period, say one year, arising from a random number N of individual insurance claims, whose sizes are described by the random variables (X n) n∈. Under the above assumptions, Wald's equation can be used to calculate the expected total claim amount when information about the average claim number per year and the average ...
In statistics, an L-estimator (or L-statistic) is an estimator which is a linear combination of order statistics of the measurements. This can be as little as a single point, as in the median (of an odd number of values), or as many as all points, as in the mean.