Logistic-Normal Distributions: Some Properties and Uses

Aitchison, J.; Shen, S. M.

doi:10.2307/2335470

Cited by 343 publications

(260 citation statements)

References 12 publications

(19 reference statements)

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“…Such properties make it indisputably the reference model for expressing the non trivial idea of substantial independence for compositions but at the same time heavily restrict its potential for applications. In the light of such inadequacies a powerful methodology based on log ratio transformations of the original variables has been proposed in [1,2]. In such an approach parametric models are built in the unconstrained transformed sample space.…”

Section: Discussion and Further Developmentsmentioning

confidence: 99%

On a class of distributions on the simplex

Favaro

Hadjicharalambous

Prünster

2011

Journal of Statistical Planning and Inference

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In the present paper we define and investigate a novel class of distributions on the simplex, termed normalized infinitely divisible distributions, which includes the Dirichlet distribution. Distributional properties and general moment formulae are derived. Particular attention is devoted to special cases of normalized infinitely divisible distributions which lead to explicit expressions. As a by-product also new distributions over the unit interval and a generalization of the Bessel function distribution are obtained.

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Section: Discussion and Further Developmentsmentioning

confidence: 99%

On a class of distributions on the simplex

Favaro

Hadjicharalambous

Prünster

2011

Journal of Statistical Planning and Inference

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“…A welcome addition to the various classes of parametric distributions on the simplexthe additive logistic normal (Aitchison and Shen, 1980;Aitchison, 1986, p.113), the multiplicative logistic normal (Aitchison, 1986, p.130), partitioned classes (Aitchison, 1986, p.132) and the Dirichlet-embracing generalisation *Aitchison, 1985*Aitchison, , 1986) -is the multivariate logistic skew normal based on the multivariate skew normal class on R D introduced by Azzalini and Dalle Valle (1996) and further developed by Azzalini and Capitanio (1999). This allows for skewness in the logratio transformed data and promises to allow more extensive study of methods which depend on distributional form.…”

Section: Probability Measures On the Simplexmentioning

confidence: 99%

Compositional Data Analysis: Where Are We and Where Should We Be Heading?

2005

Self Cite

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We take stock of the present position of compositional data analysis, of what has been achieved in the last 20 years, and then make suggestions as to what may be sensible avenues of future research. We take an uncompromisingly applied mathematical view, that the challenge of solving practical problems should motivate our theoretical research; and that any new theory should be thoroughly investigated to see if it may provide answers to previously abandoned practical considerations. Indeed a main theme of this lecture will be to demonstrate this applied mathematical approach by a number of challenging examples.

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“…As in (2.7), the conditional distribution of Y given r = K (a constant) is const Q p/2exp(I Q2 1/2 (3.13) 3 …”

Section: Pmentioning

confidence: 98%