A Study on Error Sixes and Required Sample Sixe in Sequential Probability Ratio Test Amonte Carlo Approach
| dc.contributor.advisor | Tessera, Abebe(PhD) | |
| dc.contributor.author | Dilba, Gemechis | |
| dc.date.accessioned | 2018-06-26T07:05:14Z | |
| dc.date.accessioned | 2023-11-09T14:29:48Z | |
| dc.date.available | 2018-06-26T07:05:14Z | |
| dc.date.available | 2023-11-09T14:29:48Z | |
| dc.date.issued | 1993-12 | |
| dc.description.abstract | In this paper computer simulation is employed to investigate the nature of the error sizes and the distribution of sample size required in a sequential probability ratio test (SPRT). In the test we can distinguish between two kinds of error probabilities. The first kind are the specified error probabilities which are usually denoted by a and B, and the second kind are the true error probabilities which may be denoted by at and Bt• Wald has shown that the relation at + Bt ~ a + B holds true. The objective of this project is to investigate the relation between at and a, and between Bt and B. As sample size required in SPRT is a random variable, its distribution is also studied. Two probability distributions: Bernoulli and normal (known variance) are selected for the study. The study shows that in ,t.he' case 'of norma'l' distribution, when the parameters under rio:: 5rrd' :~i' ;~re: ,sl~g~~i~ :f*~: :*p,~'tt and a = B, the estimates of true error, 'probahiIi ties, C',1:'e less 'than their corresponding specifi~d ~rror i)r('b~hi!iit~es and"that 'they are close to each other. The est:lmat,es ~t ;t' 'a'h? ~t ,~1~9 decr:ease as d = 9 1 - 90 increases. Th~s, lillJ.q~s, t~a,t, tlJ.~ ~9t~a,i ~iflks, {iz:e by far less than the specified value for large d. When a and Bare not equal, there are times when the estimate of at or Bt exceeds its corresponding specified error size as observed. But, still if the parameters under HO and HI are far apart, the estimates indicate that at ~ a and Bt ~ B. For Bernoulli distribution, the results are not very far from those of normal except that in some cases the estimates of at or Bt are found to be greater than a or B which led to disobeying the inequality at + Bt ~ a + B. This may be attributed to sample fluctuation. And finally, sample size distribution is observed to depend mainly on d = 9 1 - 9 0 (90 < 9 1). The mean and variance of the required sample size increase rapidly as d decreases. Further, the distributions are all positively skewed. It is also observed that in rare occasions there is a chance that the sample size in SPRT exceeds the size one needs in non-sequential test | en_US |
| dc.identifier.uri | http://10.90.10.223:4000/handle/123456789/3489 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Abeba university | en_US |
| dc.subject | Sequential Probability Ratio | en_US |
| dc.title | A Study on Error Sixes and Required Sample Sixe in Sequential Probability Ratio Test Amonte Carlo Approach | en_US |
| dc.type | Thesis | en_US |