English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper investigates probability density functions (PDFs) that arecontinuous everywhere, nearly uniform around the mode of distribution, andadaptable to a variety of distribution shapes ranging from bell-shaped torectangular. From the viewpoint of computational tractability, the PDF based onthe Fermi-Dirac or logistic function is advantageous in estimating its shapeparameters. The most appropriate PDF for $n$-variate distribution is of theform:$p\left(\mathbf{x}\right)\propto\left[\cosh\left(\left[\left(\mathbf{x}-\mathbf{m}\right)^{\mathsf{T}}\boldsymbol{\Sigma}^{-1}\left(\mathbf{x}-\mathbf{m}\right)\right]^{n/2}\right)+\cosh\left(r^{n}\right)\right]^{-1}$where $\mathbf{x},\mathbf{m}\in\mathbb{R}^{n}$, $\boldsymbol{\Sigma}$ is an$n\times n$ positive definite matrix, and $r>0$ is a shape parameter. Theflat-topped PDFs can be used as a component of mixture models in machinelearning to improve goodness of fit and make a model as simple as possible.

Flat-topped Probability Density Functions for Mixture Models