التفاصيل البيبلوغرافية
| العنوان: |
Explicit constants in the nonuniform local limit theorem for Poisson binomial random variables. |
| المؤلفون: |
Auld, Graeme, Neammanee, Kritsana |
| المصدر: |
Journal of Inequalities & Applications; 5/10/2024, Vol. 2024 Issue 1, p1-26, 26p |
| مصطلحات موضوعية: |
BINOMIAL theorem, LIMIT theorems, RANDOM variables, POISSON'S equation, PROBABILITY theory |
| مستخلص: |
In a recent paper the authors proved a nonuniform local limit theorem concerning normal approximation of the point probabilities P (S = k) when S = ∑ i = 1 n X i and X 1 , X 2 , ... , X n are independent Bernoulli random variables that may have different success probabilities. However, their main result contained an undetermined constant, somewhat limiting its applicability. In this paper we give a nonuniform bound in the same setting but with explicit constants. Our proof uses Stein's method and, in particular, the K-function and concentration inequality approaches. We also prove a new uniform local limit theorem for Poisson binomial random variables that is used to help simplify the proof in the nonuniform case. [ABSTRACT FROM AUTHOR] |
|
Copyright of Journal of Inequalities & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
| قاعدة البيانات: |
Complementary Index |
Full Text Finder