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Distributions generated by transformations of scale using an extended Schlömilch transformation

Jones, M. C. (2010). Distributions generated by transformations of scale using an extended Schlömilch transformation. Sankhya A : The Indian Journal of Statistics, 72(2) pp. 359–375.

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Abstract

Baker (2008) shows how more flexible densities on R+ can be generated from others by applying the Cauchy-Schlömilch transformation to the abscissa. Such “transformation of scale” is not even guaranteed to provide integrable functions in general. The appeal of the Cauchy-Schlömilch transformation is that it automatically does so; moreover, the normalising constant is unaffected and hence immediately available. In this paper, we fit the original Cauchy-Schlömilch transformation into a broader framework of novel extended Cauchy-Schlömilch transformations based on self-inverse functions, and propose the corresponding newly generated densities which also retain the same normalising constant. As well as providing parallels with, and extensions of, the many properties of the new densities developed by Baker, we investigate the skewness properties of both original and extended Cauchy-Schlömilch-based distributions via application of a recently proposed density-based approach to quantifying asymmetry.

Item Type: Journal Article
Copyright Holders: 2010 Indian Statistical Institute
Keywords: asymmetry function; life distribution; normalising constant; self-inverse function
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 25817
Depositing User: Sarah Frain
Date Deposited: 28 Dec 2010 20:53
Last Modified: 30 Nov 2012 10:44
URI: http://oro.open.ac.uk/id/eprint/25817
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