Stein's Method for Geometric Approximation
نویسنده
چکیده
The Stein-Chen method for Poisson approximation is adapted to the setting of the geometric distribution. This yields a convenient method for assessing the accuracy of the geometric approximation to the distribution of the number of failures preceding the first success in dependent trials. The results are applied to approximating waiting time distributions for patterns in coin tossing, and to approximating the distribution of the time when a stationary Markov chain first visits a rare set of states. The error bounds obtained are sharper than those obtainable using related Poisson approximations. STEIN'S METHOD; GEOMETRIC APPROXIMATION; POISSON APPROXIMATION; HITTING TIMES; PATTERNS IN COIN TOSSING AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60E15 SECONDARY 60C05; 60J10
منابع مشابه
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