확률분포의 극한성질에 관하여

Abstract

추측통계학에서 모집단의 크기 또는 표본의 크기가 무한히 클 때 극한 성질로서 나타나는 초기하분포, 이항분포, 정규분포, poisson분포, t분포, χ^(2)분포 사이의 극한성질을 밝혔다.;In this paper we prove the following theorems on the limit properties of Probability Distributions : (a) Prove that the hypergeometric distribution converges to the Binomial distribution as N→∞, where N is size of population. (b) Prove that the Binomial distribution converges to the poisson distribution as n→∞, where n is size of sample. (c) Prove that the Binomial distribution converges to the normal distribution as n→∞. (d) Prove that the Poisson distribution converges to the normal distribution as n→∞. (e) Prove that the "student" t distribution with n degrees of freedom converges to the normal distribution as n→∞. (f) Prove that the Chi-square distribution with n degrees of freedom converges to the normal distribution as n→∞.