Fiducial distribution in a power series family

Edilberto Nájera, Federico O’Reilly and Silvia Ruiz-Velasco

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 23, 5796-5808

Abstract: In this article the interest is on finding the fiducial distribution of the parameter, when the probability distribution belongs to the power series family, as in Johnson et al. (1992). Recently in Nájera and O’Reilly (2017) an argument is given to obtain a unique fiducial in the Bernoulli case. An attempt is made here to define some sort of invariance in a power series distribution so that, as was done in the Bernoulli case, one may find a unique invariant fiducial for the parameter. The Bernoulli case is reviewed in detail and the Poisson and negative binomial cases are addressed.

Date: 2019
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DOI: 10.1080/03610926.2018.1522347

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