Finding the distribution of a statistic is always an important problem that we face in statistical inference. Methods that are usually used for solving this problem are change of variable technique, distribution function technique and moment generating function technique. Among these methods change of variable technique is the most commonly used one. This method is simple when the statistic is a one-to-one transformation of the sample observations and if it is many-to-one, then one needs to compute the jacobian for each partition of the range for which the transformation is one-to-one. In addition, if we want to find the distribution of a statistic involving n random variables using the change of variable technique, we have to define (n-1) auxiliary variables. Unless these (n-1) auxiliary variables are carefully chosen, calculation of jacobian as well as finding the range of integration to obtain the marginal distribution of the statistic of interest become complicated. [See [3]]Au, Chi and Tam, Judy [1] proposed an alternative method of finding the distribution of a statistic by using Dirac generalized function. In this study we considera number of problems involving different probability distributions that are not quiet easy to solve by change of variable technique. We will illustrate the method by solving problems which include finding the distributions of sums, products, differences and ratios of random variables. The main purpose of the thesis is to show that using Dirac generalized function one can solve these problems with more ease. This alternative approach would be more suitable for students with limited mathematical background. / Department of Mathematical Sciences
| Identifer | oai:union.ndltd.org:BSU/oai:cardinalscholar.bsu.edu:handle/186717 |
| Date | January 2000 |
| Creators | Lopa, Samia H. |
| Contributors | Ali, Mir M. |
| Source Sets | Ball State University |
| Detected Language | English |
| Format | ix, 39 leaves : ill. ; 28 cm. |
| Source | Virtual Press |
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