Poisson Distribution Of The Interval Estimation Of The Parameters Analyzed

This dissertation investigates the interval estimate for the parameter in Poisson distribution, which is a basic, but important problem in mathematical statistics. On account of the importance of this subject, there has been lots of research interspersing among textbooks and literatures, and some confidence intervals accepted by people have been given. However, via intensive numerical computation, the author finds that actually some characteristic of this confidence intervals, for example, confidence coefficient, expectation width and coverage efficiency fluctuate intensely when the sample size varies given the parameter, or when the parameter varies given the sample size. When the parameter is fixed, sometimes the coverage probability may decrease with the increase of sample size, which is abnormal phenomenon, that is to say, there exists so called "unluky point". Meanwhile, it could be seen that there does not exist a confidence interval with width less than 0.5 because of the property of Poisson distribution. Based on these conditions, the author mainly carried out research into two aspects of this problem as follows. Firstly, by numerical and theoretical analysis, the author compares some existent confidence intervals, for example, "exact" confidence interval, Wald confidence interval and Bayesian confidence interval, and finds some deficiencies points of the confidence intervals, whose modification version has been proposed .Also, several better confidence intervals such asare also presented .Secondly, for given confidence coefficient and interval width, the author constructs a class of asymptotical two-stage interval estimate procedures. At the same time, under varies restriction of confidence coefflcientent interval width, the optional sample size of the first stage has been computed by numerical computation. The numerical computation shows that the method considered in this dissertation have good properties and applied value.