Asymptotics of powers of binomial and multinomial probabilities

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• 作者：K.B. Athreya^a ; ^{kba@iastate.edu" class="auth_mail" title="E-mail the corresponding author} ; R. Janicki^b ; ^{Ryan.Janicki@census.gov" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Binomial ; Multinomial ; Asymptotics
• 刊名：Statistics & Probability Letters
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：112
• 期：Complete
• 页码：58-62
• 全文大小：360 K

文摘

Fix positive integers aead535cc91817defe13a5bba6ded5" title="Click to view the MathML source">k≥2$k\ge 2$, 6aec45ce6c" title="Click to view the MathML source">j≥2$j\ge 2$ and numbers p₁,p₂,…,p_k$p_1,p_2,\dots ,p_k$ such that 0<p_i<1$0<p_i<1$ for all i=1,2,…,k$i=1,2,\dots ,k$, and ${\sum }_{i=1}^k{p}_i=1$. For a positive integer n$n$, let where 6ad125b4e5de37fa8ed2efd4700999" title="Click to view the MathML source">T_n,k$T_{n,k}$ is the set $\{(n_1,n_2,\dots ,n_k):n_i\in \{0,1,2,\dots ,n\},{\sum }_{i=1}^k{n}_i=n\}$. Then there exists 0<b_j,k(p₁,p₂,…,p_k)<∞$0<b_{j,k}(p_1,p_2,\dots ,p_k)<\infty$ such that as n→∞$n\to \infty$.