The proposed test called ELT is a goodness of fit test for discriminating between the family of the extended exponential geometric (EEG) distributions and the family of the Gamma distributions. The corresponding test statistic is developed based on the empirical Laplace transform () ktx e (, ) txwhere the argument value maximizes n X () ; t L t and is replaced by its MLE . It is verified that converges in distribution to (0 , 1). Performance of the proposed test is compared via Monte Carlo studies to that of the Kolmogorov – Smirnov (KS) test and ...