Comments On "Testing a Sample Population for the Rayleigh Distribution" and a Succeeding Correction

In a recent correction [2] to previous correspondence [1] it was stated that 3) of the theorem in [1] was invalid due to the statistical dependence of the yi. The joint distribution function of the yiis derived below confirming their dependence, but also upholding the validity of Item 3. Furthermore, an exact goodness of fit test for the Rayleigh distribution based upon theN + 1observationsx_{1}, ... , x_{N+1}is suggested.