2 I recently became interested in this definition in trying to make rigorous my answer to this Question. In the univariate case a notion of unimodal function is generalized from that of a …

May 2, 2020 · Now I wanted to prove that this function is unimodal but I am unable to do so. Actually, I was learning Ternary Search so I wanted to apply that technique to a problem and …

Unimodality of q-binomial coefficients is a difficult theorem, proved more than 20 years after it was conjectured. If you're really interested in a proof — it's easy to google references.

Oct 29, 2020 · It is best to write this generating function as $$ \frac1 {1-q}\cdot \frac1 {1-q^2}\cdots \frac1 {1-q^ {k-1}}\cdot \frac {q^k} {1-q^k}\cdot \frac1 {1-q^ {k-1}}\cdots \frac1 {1-q} $$ Expand …

Sep 7, 2024 · (Proof review) The product of symmetric unimodal polynomials is again symmetric unimodal. Ask Question Asked 1 year, 2 months ago Modified 1 year, 2 months ago

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 …

May 4, 2016 · Normal distributions are always unimodal. It looks like by "bimodal normal data" you mean a Gaussian Mixture Model (GMM) with 2 components (i.e. the PDF of the data is a …

Jul 28, 2015 · Properties of unimodal functions Ask Question Asked 10 years, 4 months ago Modified 2 years, 6 months ago

Mar 20, 2023 · If the distribution is both symmetric and unimodal, the mode also coincides with $\mu,m$. For general distributions, there are many examples that break the rules of thumb …

Note that in both cases there can be more than one mode, since the maximum value of either the pmf or the pdf can be attained at more than one value. If there is a single mode, the …