To test whether a set of data has a specific distribution or not, we can use the goodness of fit test. This test can be done by one of Pearson X2-statistic or the likelihood ratio statistic G2, which are asymptotically equal, and also by using the Kolmogorov-Smirnov statistic in continuous distributions. In this paper, we introduce a new test statistic for goodness of fit test which is based on entropy distance, and which can be applied for large sample sizes. We compare this new statistic with the classical test statistics X2, G2, and Tn by some simulation studies. We conclude that the new statistic is more sensitive than the usual statistics to the rejection of distributions which are al- most closed to the desired distribution. Also for testing independence, a new test statistic based on mutual information is introduced.

Goodness-of-fit tests are constructed for the two-parameter Birnbaum-Saunders distribution in the case where the parameters are unknown and therefore are estimated from the data. In each test, the procedure starts by computing e cient estimators of the parameters. Then the data are transformed by a normal transfor-mation and normality tests are applied on the transformed data, thereby avoiding reliance on parametric asymptotic critical values or the need for bootstrap computa-tions. Three classes of tests are considered, the first class being the classical tests based on the empirical distribution function, while the other class utilizes the empirical char-acteristic function and the final class utilizes the Kullback-Leibler information function. All methods are extended to cover the case of generalized three-parameter Birnbaum-Saunders distributions.