In [14], Sanov proved that if FN is the empirical cumulative distribution function (cdf) of a sample drawn from a population whose true cdf is F0 and Ω is a set of cdf's which satisfies certain ...

In this paper, we consider the function f p ( t )= 2p X 2 ( 2p t+p;p ) , where χ²(x; n) defined by X 2 ( x;p )= 2 −p/2 Γ( p/2 ) e −x/2 x p/2−1 , is the density function of a χ²-distribution with n ...

What happened when a gambler asked for help from a mathematician? The formal study of Probability. Infinite Series is available to stream on pbs.org and the free PBS App, available on iPhone, Apple TV ...

Ruin theory has emerged as a pivotal branch of actuarial science, offering a robust mathematical framework to quantify the risk of insolvency in both insurance and financial contexts. At its core, the ...