Muraleedharan Nair,K R; Dr.Unnikrishnan Nair, N(Cochin University Of Science And Technology, May 10, 1990)
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Abstract:
It is highly desirable that any multivariate
distribution possessescharacteristic properties that
are generalisation in some sense of the corresponding
results in the univariate case. Therefore it is of
interest to examine whether a multivariate distribution
can admit such characterizations. In the exponential
context, the question to be answered is, in what meaning—
ful way can one extend the unique properties in the
univariate case in a bivariate set up? Since the lack
of memory property is the best studied and most useful
property of the exponential law, our first endeavour
in the present thesis, is to suitably extend this
property and its equivalent forms so as to characterize
the Gumbel's bivariate exponential distribution.
Though there are many forms of bivariate exponential
distributions, a matching interest has not been shown
in developing corresponding discrete versions in the
form of bivariate geometric distributions. Accordingly,
attempt is also made to introduce the geometric version
of the Gumbel distribution and examine several of its
characteristic properties. A major area where exponential
models are successfully applied being reliability
theory, we also look into the role of these bivariate
laws in that context.
The present thesis is organised into five
Chapters
Description:
Department of Mathematics
and Statistics, Cochin University of Science
and Technology