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- W4247409982 abstract "Abstract This chapter gives examples of probability distributions that, in their conventional parametrization, contain embedded models. Embeddedness is not intrinsic but depends on the parametrization. The simplest way to reveal and remove embeddedness is to reparametrize and make the log-likelihood, L, expandable as a Maclaurin series of one parameter, α: L = L0 + L1α + L2 α2 + … with L0 the log-likelihood of the embedded model hidden in the original parametrization. The quantity L1, rescaled using the information matrix, is the score statistic which can be used for formally comparing the original and embedded model fits. Embeddedness occurs in many distributions if there is a shifted threshold parameter. Examples given in the chapter are the Burr XII, gamma, generalized extreme value, inverse Gaussian, inverted gamma, logistic, loglogistic, lognormal, loggamma, Pareto, and Weibull distributions. Another interesting example occurs in early parametrizations of the stable law distribution." @default.
- W4247409982 created "2022-05-12" @default.
- W4247409982 creator A5044273453 @default.
- W4247409982 date "2017-06-22" @default.
- W4247409982 modified "2023-09-29" @default.
- W4247409982 title "Examples of Embedded Distributions" @default.
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- W4247409982 doi "https://doi.org/10.1093/oso/9780198505044.003.0006" @default.
- W4247409982 hasPublicationYear "2017" @default.
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