In order to introduce left and right truncated versions of the modified lognormal with a power-law distribution, we derive its probability density function, its distribution function, its average value, its second moment of the origin, its variance, how to randomly generate its values, the maximum likelihood and the nonlinear least squares estimators for its three unknown parameters. It is then applied to five clusters of stars, to the mass function for stars, and to one catalog for the masses of the galaxies.
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