Exponential exact estimation for maximum and minimum tail of distribution for non-Gaussian random vector

TL;DR

This paper derives an exact exponential two-term non-asymptotic expression for the maximum and minimum distribution tails of a non-Gaussian random vector, providing precise probabilistic bounds.

Contribution

It introduces a novel exponential exact formula for the tail distributions of non-Gaussian random vectors, extending beyond Gaussian assumptions.

Findings

Derived explicit two-term exponential expressions for tail probabilities.

Applicable to non-Gaussian random vectors in general cases.

Provides non-asymptotic probabilistic bounds.

Abstract

We find the exponential exact two-terms non-asymptotic expression for the maximum and minimum distribution of a non-Gaussian, in general case, random vector.