臺灣博碩士論文加值系統

Statistical applications and repercussions of the
Poisson distribution. In this thesis, we introduce the
relationship between the Poisson distribution and the Binomial ,
Negative Binomial, and hypergeometric distributions. Moreover, we
consider the Poisson approximation to the distribution of the sums
of iid Bernoulli / geometric and non-identically distributed
random variables.

1.Introduction 3
2. Some Discrete Distribution 5
2.1 Bernoulli Trials 6
2.2 Binomial Distribution 7
2.3 Geometric Distribution 9
2.4 Negative Binomial Distribution 10
2.5 Poisson Distribution 12
3. The Poisson Approximation for Sums of Independent and Identically
Distributed Random Variables 16
3.1 Limits of the Binomial Distributions 17
3.2 Limits of the Negative Binomial Distribution 26
3.3 Limits of the Hypergeometric Distributions 27
4. The Poisson Approximation for Sums of Independent but Non-Identically Distributed Random Variables 28

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