Statistical power of an information-based test and its application to wave height data

Modeling wave heights is crucial for many maritime applications. An appropriate statistical distribution for describing wave heights is the Rayleigh distribution. Estimating and testing the significance of the parameters of a distribution are important in statistical modeling and allow meaningful predictions about uncertain events. We propose an information-based method to test the significance of parameters of a given one-dimensional distribution. The power of the proposed test is compared to that of the likelihood ratio tests for hypotheses on the parameters of the exponential and Rayleigh distributions. Monte Carlo simulations demonstrate that the proposed method yields a satisfactory power level that is comparable to that of the likelihood ratio test. The method is illustrated using real wave height data.