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A Method for Bounding Tail Probabilities
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DOI：10.1109/ACCESS.2026.3650974.png)
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Abstract
En 中文
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 RVXwith probability density functionf(x), this method requires first setting a continuous, positive, and strictly decreasing functiong (x) such that-f(x)/g '(x) is a decreasing and increasing function,for all x>x0, which results in upper and lower bounds,respectively, given in the form-f(x)g(x)/g '(x),for all x>x0, wherex0is some point. Similarly, for the upperand lower bounds on the left tail probability of X, this method requires first setting a continuous, positive, andstrictly increasing functiong(x) such thatf(x)/g '(x) is an increasing and decreasing function, for all x
Keywords:
Lower bound
Upper bound
Channel capacity
AWGN channels
Probability density function
Iterative methods
Random variables
Error analysis
Signal to noise ratio
Reliability theory
Tail probabilities
tail bounds
continuous random variables