Non uniform exponential bounds on normal approximation by Stein's method and monotone size bias couplings

作者：Kamjornkittikoon Kamonrat; Neammanee Kritsana^*; Chaidee Nattakarn

来源：Communications in Statistics - Theory and Methods, 2018, 47(5): 1117-1132.

DOI：10.1080/03610926.2017.1316404

• Lightbulb process
• Monotone size bias couplings
• Non uniform exponential bound
• Normal approximation
• m runs
• Stein's method

It is known that the normal approximation is applicable for sums of non negative random variables, W, with the commonly employed couplings. In this work, we use the Stein's method to obtain a general theorem of non uniform exponential bound on normal approximation base on monotone size bias couplings of W. Applications of the main result to give the bound on normal approximation for binomial random variable, the number of bulbs on at the terminal time in the lightbulb process, and the number of m runs are also provided.

• 出版日期2018