A General Approximation for the Distribution of Count Data
نویسندگان
چکیده
Under mild assumptions about the interarrival distribution, we derive a modi ed version of the Birnbaum-Saunders distribution, which we call the tBISA, as an approximation for the true distribution of count data. The free parameters of the tBISA are the rst two moments of the underlying interarrival distribution. We show that the density for the sum of tBISA variables is available in closed form. This density is determined using the tBISA's moment generating function, which we introduce to the literature. The tBISA's moment generating function additionally reveals a new mixture interpretation that is based on the inverse Gaussian and gamma distributions. We then show that the tBISA can t count data better than the distributions commonly used to model demand in economics and business. In numerical experiments and empirical applications, we demonstrate that modeling demand with the tBISA can lead to better economic decisions.
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