期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2010
卷号：72
期号：02
页码：359--375
出版社：Indian Statistical Institute
摘要：Baker (2008) shows how more exible densities on .. + can be generated from
others by applying the Cauchy-Schlomilch transformation to the abscissa.
Such \transformation of scale" is not even guaranteed to provide integrable
functions in general. The appeal of the Cauchy-Schlomilch transformation
is that it automatically does so; moreover, the normalising constant is una
ected and hence immediately available. In this paper, we t the original
Cauchy-Schlomilch transformation into a broader framework of novel extended
Cauchy-Schlomilch 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-
Schlomilch-based distributions via application of a recently proposed densitybased
approach to quantifying asymmetry.
关键词：Asymmetry function, life distribution, normalising
constant, self-inverse function.
