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This paper describes a simple procedure to estimate the parameters of theunivariate truncated normal and lognormal distributions by maximum likelihood.It starts from a reparameterization of the lognormal that was previouslyintroduced by the author and is especially useful when the lognormal is closeto a power law, which is a limiting case of the first distribution. One of thenew parameters quantifies the distance from the power law, and vanishes whenthe power law gives a sufficient description of the data. At this point, theother parameter equals the exponent of the power law. In contrast, when usingthe standard parameterization, the parameters of the lognormal diverge in theneighborhood of the power law. Whether or not we are in this neighborhood, thenew parameters have properties that ease the process of estimation.

Algorithm for the maximum likelihood estimation of the parameters of the truncated normal and lognormal distributions