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Let K be a random variable following a truncated exponential distribution.Such distributions are described by a single parameter here denoted by$\gamma$. The determination of $\gamma$ by Maximum Likelihood methods leads toa transcendental equation. We note that this can be solved in terms of theinverse Langevin function. We develop approximations to this guided by work ofSuehrcke and McCormick.

The Langevin function and truncated exponential distributions