A probability density function is developed for the phase of light that is the result of adding a signal to noise with K-distributed amplitude and uniform phase. The probability density function of the phase associated with the I-K distribution is also developed. In the process of deriving the probability density function of the phase much I as learned about the relationships between different probability density functions. Three different methods of deriving homodyned K statistics are shown to be equivalent. Two different methods of deriving I-K statistics are shown to be equivalent. Theoretical moments of the homodyned K distribution are compared with experimentally measured moments in order to determine the parameters of the model for different conditions of turbulence. An experiment is proposed for measuring the spatial structure function of the phase in a manner that will allow verifying the accuracy of the new probability density functions of the phase.