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The following are among the properties of log-concave distributions: If a density is log-concave, so is its cumulative distribution function (CDF). If a multivariate density is log-concave, so is the marginal density over any subset of variables. The sum of two independent log-concave random variables is log-concave. This follows from the fact ...
Using the fact that (,) =, the generalized Marcum Q-function can alternatively be defined as a finite integral as (,) = (+) ().However, it is preferable to have an integral representation of the Marcum Q-function such that (i) the limits of the integral are independent of the arguments of the function, (ii) and that the limits are finite, (iii) and that the integrand is a Gaussian function ...
This is the source of the log-concave restriction: if a distribution is log-concave, then its logarithm is concave (shaped like an upside-down U), meaning that a line segment tangent to the curve will always pass over the curve. If not working in log space, a piecewise linear density function can also be sampled via triangle distributions [8]
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Log-concave may refer to: Logarithmically concave function ...
The Brunn–Minkowski inequality asserts that the Lebesgue measure is log-concave. The restriction of the Lebesgue measure to any convex set is also log-concave.. By a theorem of Borell, [2] a probability measure on R^d is log-concave if and only if it has a density with respect to the Lebesgue measure on some affine hyperplane, and this density is a logarithmically concave function.
Later, the ability to show all of the steps explaining the calculation were added. [6] The company's emphasis gradually drifted towards focusing on providing step-by-step solutions for mathematical problems at the secondary and post-secondary levels. Symbolab relies on machine learning algorithms for both the search and solution aspects of the ...
In mathematics, a sequence a = (a 0, a 1, ..., a n) of nonnegative real numbers is called a logarithmically concave sequence, or a log-concave sequence for short, if a i 2 ≥ a i−1 a i+1 holds for 0 < i < n. Remark: some authors (explicitly or not) add two further conditions in the definition of log-concave sequences: a is non-negative
To find the needed , , , and the algorithm uses Floyd's cycle-finding algorithm to find a cycle in the sequence =, where the function: + is assumed to be random-looking and thus is likely to enter into a loop of approximate length after steps.