We have carried out numerical simulations of waves traversing a 3D random medium with Gaussian statistics and a power-law spectrum with inner-scale cutoff. The distributions of irradiance on the final observation screen provide the probability density function (PDF) of irradiance, which includes the first few moments of irradiance and In-irradiance. Analytic calculations to third order by a path-integral technique are in excellent agreement with these moments. Experimental measurements of irradiance variance as a function of turbulence strength and inner scale for both initially plane and initially spherical waves in the strong-fluctuation regime are in excellent agreement with the simulation variances. The simulation PDFs in the strong- fluctuation regime lie between a K-distribution and a lognormal- convolved-with-exponential distribution. We introduce a plot of the PDF of scaled In-irradiance, on which both the exponential and lognormal PDFs are universal curves, and on which the PDF at both large and small irradiance is shown in detail. We have simulated a spherical-wave experiment, including aperture averaging, and find agreement between the simulated and observed PDFs.
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