Abstract
This chapter looks at positive (0-truncated), zero-inflated and zero-altered (hurdle) distributions, with the focus on discrete distributions. Zero-deflated distributions are also mentioned. Specific examples include the zero-inflated Poisson and positive-binomial distributions. Another example concerns closed-population capture–recapture estimation, which is described in relatively more detail as an application of a positive-Bernoulli distribution. Reduced-rank variants of some of the above models are also considered.
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The location parameter of an exponential distribution must be treated as known. Due to the memoryless property, it would be unestimable if unknown. And if unknown, the regularity conditions would be violated as the support depends on it.
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Yee, T.W. (2015). On VGAM Family Functions. In: Vector Generalized Linear and Additive Models. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2818-7_18
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DOI: https://doi.org/10.1007/978-1-4939-2818-7_18
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