A Monte Carlo Study of the Properties of Selected Tests Based on Sample Spacings
Author | : Kweku Ewusi-Mensah |
Publisher | : |
Total Pages | : 0 |
Release | : 1972 |
ISBN-10 | : OCLC:1446384643 |
ISBN-13 | : |
Rating | : 4/5 (43 Downloads) |
Book excerpt: Let X[subscript 1], X[subscript 2] ... X[subscript n] be n independent random variables each distributed uniformly over the interval (0,1) and let D[subscript 1], D[subscript 2] ... D[subscript n+1] respective spacings of the (n+1) intervals into which the unit interval is divided. There exists a class of statistical problems related to finding the distribution of certain functions of the D[subscript i]. A review of these statistical tests is given in Chapter II. In deriving the properties of the statistics, it is usually assumed that, because the underlying distribution of D[subscript i] is continuous, the problem of tied observations does not arise. However this is a problem the statistician has to face in actual data situations. We have, in this study evaluated the sensitivity of the test statistics to ties and grouping errors. We have also considered how robust the statistics are by evalua- ting their sensitivity under the X[2 over 2] normal (0,1) distributions. The result of this test for robustness will give the applied statistician a valid basis for using the statistics in tests of hypothesis other than those involving the uniform (0,1) distribution. For completeness we have also looked at ties and grouping errors under discrete distributions. In this case the sensitivity of the statistics to the different tie breaking rules is found to depend quite heavily on the number of ties occurring in the data. The Monte Carlo method was used in attacking the problem and results are given in Chapters IV and V.