This text on inverted distributions and Theory of Inversion relates
to the early work of Snedecor (1934), Merington and Thomson (1943).
Since 1934 very little attention has been paid to this area, though
some work has been done in eighties and nineties. In this book we
discuss a theoretical framework for distributions closed under
inversion, reviewed inverted distributions and present some
concepts of closure and strict closure under inversion (CUI and
SCUI). We provide the details of pervious work done by Gumbel and
Keeney (1950), Seshadri (1950) and Saunders (1974). We investigate
the intrinsic nature of SCUI distributions and present (a) a set of
differential equations for generating SCUI distributions, (b) some
characterization theorems for SCUI density functions, and (c) a few
properties common to all SCUI distributions. We extend a number of
concepts relating to SCUI distributions to the CUI case.
General
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