3
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1answer
51 views

Inequalities for the tail of the normal distribution (Halfin-Whitt paper)

I am reading the famous paper by Halfin and Whitt, [1]. I'd like to prove remark (1) on page 575. The authors state \begin{align} \frac{\beta \alpha}{(1-\alpha)} = \frac{\phi(\beta)}{\Phi(\beta)} ...
1
vote
1answer
151 views

Chernoff bound for Geometric RVs compared to exact tail bound

I keep getting a result I can't interpret. X is a Geometric RV with distribution ($0<\rho<1$) $$ \pi_k = \rho^k(1- \rho) $$ so directly applying Geometric series the tail bound is $$ B_1 = ...