The fading characteristics of ionospheric amplitude scintillations can be described by a cumulative amplitude probability distribution function (cdf). The cdf expresses the probability (percentage of time) that the signal amplitude will equal or exceed a given amplitude. Distributions of amplitude variations are made with the use of ionospheric scintillations observed on beacon signals from synchronous satellites transmitting at 136 MHz. The resulting distributions are divided into six groups corresponding to ranges of the scintillation index, the predominant measure in scintillation studies. The model distributions are then combined with the occurrence of scintillations in various index ranges to produce cumulative amplitude probability distributions. These have been done for long-term observations made at Hamilton, Massachusetts, Narssarssuaq, Greenland, and Huancayo, Peru. The results allow engineers to determine margins necessary for communication and navigation systems. Individual 15-min distributions have been compared to the theoretical distributions obtained by Nakagami  in his m-distribution method of characterizing amplitude scintillation and were found to be in good agreement. The m parameter is shown to be a measure of the frequency dependence of scintillations and can be used to determine a spectral index for interpolating the amplitude distributions to other frequencies of interest.