A New Type Of Upper And Lower Bounds On Right-Tail Probabilities Of Continuous Random Variables
In this paper, I present a completely new type of upper and lower bounds on the right-tail probabilities of continuous random variables with unbounded support and with semi-bounded support from the left. The presented upper and lower right-tail bounds depend only on the probability density function (PDF), its first derivative, and two parameters that are used for tightening the bounds. These tail bounds hold under certain conditions that depend on the PDF, its first and second derivatives, and the two parameters. The new tail bounds are shown to be tight for a wide range of continuous random variables via numerical examples.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A Method For Bounding Tail Probabilities
We present a method for upper and lower bounding the right and the left tail probabilities of continuous random variables (RVs). For the right tail probability of RV $X$ with probability density function $f_X(x)$, this m…
On the Non-asymptotic and Sharp Lower Tail Bounds of Random Variables
The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds …
On the Number of Observation Nodes in Boolean Networks
A Boolean network (BN) is called observable if any initial state can be uniquely determined from the output sequence. In the existing literature on observability of BNs, there is almost no research on the relationship be…
On the Optimal Bounds for Noisy Computing
We revisit the problem of computing with noisy information considered in Feige et al. 1994, which includes computing the OR function from noisy queries, and computing the MAX, SEARCH and SORT functions from noisy pairwis…
Exponential tail bounds and Large Deviation Principle for Heavy-Tailed U-Statistics
We study deviation of U-statistics when samples have heavy-tailed distribution so the kernel of the U-statistic does not have bounded exponential moments at any positive point. We obtain an exponential upper bound for th…