real analysis - Definition of a function being unimodal
In the univariate case a notion of unimodal function is generalized from that of a unimodal distribution, which qualitatively is described as a density function "having one mode and one peak". Project Euclid hosts a paper Multivariate Unimodality by S. W. Dharmadhikari and Kumar Jogdeo (1976) which reviews the literature to that point and ...
Distinguishing between unimodal and bimodal normal data
2016年5月4日 · The only problem is, when the algorithm is fed a unimodel distribution, it doesn't really converge to just one distribution (or two very close ones). The number I'm mostly interested in, is the delta between the two means, and so in the case of a unimodal distribution, the delta-mean is overestimated.
unimodality and continuous - Mathematics Stack Exchange
If there is a single mode, the distribution function is called "unimodal". If it has more modes it is "bimodal" (2), "trimodal" (3), etc., or in general, "multimodal".
combinatorics - Unimodal Sequences - Mathematics Stack Exchange
2020年10月29日 · And let a strict unimodal sequence have the same definition, except with < instead of $\leq$, ...
More elegant solution for showing that a distribution is unimodal
2018年5月12日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
combinatorics - Unimodality of q-binomial coefficients
We also usually normalize things so all minimal elements of the poset have rank zero. Finally, a poset is called rank-unimodal if the sequence of sizes of the ranks is unimodal, increasing up to a widest point in the poset's middle and decreasing thereafter.
Efficient algorithm to find maximum of a unimodal sequence
This Wikipedia page describes the "Golden section search" for unimodal functions. Binary search is not likely to give the best worst-case behaviour. I suspect that the fastest algorithm (with the fewest array accesses in the worst case) involves the golden ratio $\varphi = (1 + \sqrt 5)/2$.
How to prove quasi-convex if and only if unimodal?
This is false as stated. Quasiconvexity definition says that the lower level sets $\{f\le \lambda\}$ are convex.
Is the sum of independent unimodal random variables still …
As Henning Makholm points out, the result is not true in general. I believe that if the independent random variables have identical unimodal distributions that are symmetrical about the mode, the sum will have unimodal distribution that is symmetric about the mode, but I don't have a proof worked out in detail.
Is double integral of Gaussian distribution over an area unimodal …
2023年3月1日 · Consider this counter-example: a ball centered at the origin and a concentric annular ring. The annular subregion is defined by $2<r<3$ and the ball has radius 1/2.