Goodness of Fit Test and Test of Independence by Entropy

To test whether a set of data has a specific distributionor not, we can use the goodness of fit test. this test can be done byone of pearson x^ 2-statistic or the likelihood ratio statistic c2, whichare asymptotically equal, and also by using the kolmogorov-smirnovstatistic in continuous distributions. in this paper, we introduce a newtest statistic for goodness of fit test which is based on entropy distance,and which can be applied for large sample sizes. we compare this newstatistic with the classical test statistics x^ 2, c62, and t'; by some simulationstudies. we conclude that the new statistic is more sensitivethan the usual statistics to the rejection of distributions which are almostclosed to the desired distribution. also for testing independence,a new test statistic based on mutual information is introduced.