DAU Library

학위논문 동서

미분연산자를 사용한 이산확률분포의 적률계산법

김재도

부산: 동아대학교 1994. -

26장; 27cm. -

학위논문(석사)- 동아대학교 교육대학원 수학교육전공 94년6월

영문초록 : The moments of probability distribution are necessary value in the process of the estimation and the process of the test, We have generally used the moment generating function and the characteristic function to get the moment. With most of the moment generating functions obtained with these methods, we can find the moments that we need. But, we have had difficuties as the following in hypergeometric distribution (1) in hypergeometric distribution a case that we can't obtain the moments and, (2) a case that the calculation of the moments is complicated according to the probability distribution. To solve these problems, in 1981, Link[8] published the new way to calculate the moment of discrete probability distribution, using the finite difference operator. Which makes it possible to calculate the moment of probability distribution more easily. Also it actually showed we could get the moment of hypergeometric distribution with it. In 1982 Chan[3] and Rao, Janardan(1982) [10], Janardan(1984) [6] and Chralmb ides(1984, 1986) [4] had improved this method, using the finite difference operator. They found out that, in case (1), the calculation of the moment of hypergeometric distribution became possible, and that there was a much easier case to calculate the moments in case (2). But this method could be used only in the discrete probability distribution. In later studies about this problem, the method has been developed that can get the moments of each type of probability distribution and the study that can get various moments, that is, descending or ascending factorial moments. In 1992 Boullion[1] published the different view, which wag the new method calculating the moment, using the differential operator. In this paper, we are going to study whether it is possible to calculate the moment or not, using the differential operator and to calculate various moments in all the probability distributions. In Chapter 2 of this study, we define the differential operator and introduce the way to use it in the calculation of the moment. In Chapter 3 we can see the moments of probability distribution which can be calculated in the various discrete probability distributions. In Chapter 4 we introduced the solution, according to the various types of moments of probability distributions which were divided. Lastly in Chapter 5, the write is going to figure out if we can get the moments with the calculation of moments, using a differential operator more easily, comparing with many other ways used in the moment calculation.

바로가기