|
||||||
REVIEW OF PUBLICATIONS
The research work of Andreas Philippou is centered in the following
areas: 1. Asymptotic Distribution Theory and Inference. 2. Exact Distribution Theory. 3. Fibonacci Polynomials with Probability and
Reliability Applications. Almost all of
his work is classified according to Mathematical Reviews and Zentralblatt fur
Mathematik as probability and /or statistics, while a few papers are classified
as number theory or operations research. One is classified as History of
Mathematics. 1. Asymptotic Distribution Theory and
Inference. His main contribution in this area lies in the study, for the
case of independent but not necessarily identically distributed random
variables, of the asymptotic behavior of the
log-likelihood function Λn(θ) and
a random vector Δn(θ) which is related to it. The
asymptotic properties of the maximum likelihood estimate (MLE) and problems of
testing simple statistical hypotheses against one-sided and two-sided
alternatives were also studied for the same case. The asymptotic properties of
the MLE have been studied for the dependent case too. 2. Exact
Distribution Theory. His main contribution in this area is, as noted by
several researchers, his pioneering work on univariate and multivariate
distributions of order k, type I and type II (geometric, binomial (linear and
circular), negative binomial, Poisson, logarithmic, Polya and inverse Polya).
Each one of them is an infinite family of distributions, which reduces to the
respective classical distribution for k=1. As a by-product of his univariate
binomial distributions of order k (linear and circular), he has derived exact
reliability formulas for linear and circular m-consecutive-k-out-of-n: F
systems. He has also derived exact formulas for the probability distribution
functions of the succession quota sooner and later waiting time random
variables in the cases of (a) Markov dependent trials and (b) a binary sequence
of order k (both of which include the independent Bernoulli trials as a special
case). Present work is focusing on generalized distributions of order k
(univariate and multivariate) and distributions of l-overlapping success runs
of length k in linear and circular arrangements, as well as runs in
Polya-Eggenberger schemes. 3. Fibonacci Polynomials with Probability and Reliability Applications. His main contribution in this area lies in the results derived on distributions of order k and systems reliability. The introduction and study of several polynomials, i.e. the Fibonacci-type polynomials of order k, the multivariate Fibonacci polynomials of the same order, the Fibonacci-type polynomials of order (k, r), and the multivariate Pascal polynomials of order k, has its own merits. The above all have been used as tools for the investigation of distributions of order k, longest runs and systems reliability. He has also started the international conferences on Fibonacci numbers and their applications in 1984 and served as co-editor of their proceedings until 1998. He continued serving as their co-chairman until 2004. |