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We considered a gammadistribution of interspike intervals as a statistical model for neuronal spike generation. A gamma distribution is a natural extension of the Poisson process taking the effect of a refractory period into account. The model is specified by two parameters: a time-dependent firing rate and a shape parameter that characterizes spiking irregularities of individual neurons. Because the environment changes over time, observed data are generated from a model with a time-dependent firing rate, which is an unknown function. A statistical model with an unknown function is called a semiparametric model and is generally very difficult to solve. We used a novel method of estimating functions in information geometry to estimate the shape parameter without estimating the unknown function. We obtained an optimal estimating function analytically for the shape parameter independent of the functional form …