This study reveals for the first time the essential mechanism of tool-integrated reasoning through rigorous mathematical proof and develops a novel training algorithm that enables AI to utilize tools ...

This research reveals, for the first time, the essential mechanisms of tool-integrated reasoning through rigorous ...

Efficient Sequential and Batch Estimation of Univariate and Bivariate Probability Density Functions and Cumulative Distribution Functions along with Quantiles (Univariate) and Nonparametric ...

A probability density function (PDF) describes the likelihood of different outcomes for a continuous random variable.

Generalized Probability Density Function Estimation via Convex Optimization A longstanding problem in statistics pertains to the estimation of probability density functions of continuous random ...

At the moment, we are trying to solve the teacher shortage without all the key information. Here are four questions we need to answer to really address this issue.

Given the characteristic function of a continuously distributed random variable, the authors showed that it is possible - using the Euler’s identity, to approximate pointwise the probability density ...

Hello, I am trying to generate Probability Density Functions (PDF) for local seismic stations. I am a little confused about that. I have read that Obspy can generate Probabilistic Power Spectral De ...