Expansions for the distributions of some normalized summations of random numbers of i.i.d. random variables
Abbreviated Journal Title
Ann. Inst. Stat. Math.
central limit theorem; expansion of a tail probability; martingale; renewal theory; sequential analysis; stopping time; Wald's lemma; ASYMPTOTIC EXPANSIONS; Statistics & Probability
The central limit theorem for a normalized summation of random number of i.i.d. random variables is well known. In this paper we improve the central limit theorem by providing a two-term expansion for the distribution when the random number is the first time that a simple random walk exceeds a given level. Some numerical evidences are provided to show that this expansion is more accurate than the simple normality approximation for a specific problem considered.
Annals of the Institute of Statistical Mathematics
"Expansions for the distributions of some normalized summations of random numbers of i.i.d. random variables" (2002). Faculty Bibliography 2000s. 3531.