On a New Goodness-of-fit Test for the Rayleigh Distribution Based on a Conditional Expectation Characterization

We propose and study new goodness-of-fit tests for the Rayleigh distribution based on a characterization involving a conditional expectation. The asymptotic properties of the tests are explored and the performance of the new tests are evaluated and compared to that of existing tests by means of a Monte Carlo study. It is found that the newly proposed tests perform satisfactory compared to the competitor tests.