1
1726-4057
Iranian Statistical Society
122
60: Probability theory and stochastic processes
Empirical Bayes Estimators with Uncertainty Measures for NEF-QVF Populations
Crescenzi
Michele
Ghosh
Malay
Maiti
Tapabrata
1
3
2005
4
1
1
19
22
10
2011
12
09
2015
The paper proposes empirical Bayes (EB) estimators for
simultaneous estimation of means in the natural exponential family
(NEF) with quadratic variance functions (QVF) models. Morris
(1982, 1983a) characterized the NEF-QVF distributions which include
among others the binomial, Poisson and normal distributions.
In addition to the EB estimators, we provide approximations to the
MSE’s of these estimators. Our approach generalizes the findings of
Prasad and Rao (1990) for the random effects model where only area
specific direct estimators and covariates are available. The EB estimators
are derived using the theory of optimal estimating functions
as proposed by Godambe and Thompson (1989). This is in contrast
to the approach of Morris (1988) who found some approximate EB
estimators for this problem. Also, unlike Morris (1988), we allow unequal
number of observations in different clusters in the derivation of
the EB estimators. In finding approximations to the MSE’s, we apply
a bias-correction technique as proposed in Cox and Snell (1968). We illustrate our methodology by reanalyzing the toxoplasmosis data of
Efron (1978, 1986).
123
60: Probability theory and stochastic processes
Record Range of Uniform Distribution
Ahsanullah
M.
1
3
2005
4
1
21
34
22
10
2011
12
09
2015
We consider a sequence of independent and identicaly
distributed (iid) random variables with absolutely continuous distribution
function F(x) and probability density function (pdf) f(x). Let
Rnl be the largest observation after observing nth record and R(ns) be
the smallest observation after observing the nth record. Then we say
Wnr = Rnl− R(ns), n > 1, as the nth record range. We will consider
some distributional properties of Wnr when f(x) = 1.
124
60: Probability theory and stochastic processes
Some New Results on Stochastic Orderings between Generalized Order Statistics
Khaledi
Baha-Eldin
1
3
2005
4
1
35
49
22
10
2011
12
09
2015
In this paper we specify the conditions on the parameters
of pairs of gOS’s under which the corresponding generalized order
statistics are ordered according to usual stochastic ordering, hazard
rate ordering, likelihood ratio ordering and dispersive ordering. We
consider this problem in one-sample as well as two-sample problems.
We show that some of the results obtained by Franco et al. [Probab.
Engrg. Inform. Sci. 2002, 16, 471-484] and Belzunce et al. [Probab.
Engrg. Inform. Sci. (2004), to appear] for stochastic orderings of
gOS’s are contained in our new results
125
60: Probability theory and stochastic processes
A Further Note on Runs in Independent Sequences
Smythe
R. T.
1
3
2005
4
1
51
56
22
10
2011
12
09
2015
Given a sequence of letters generated independently from
a finite alphabet, we consider the case when more than one, but not
all, letters are generated with the highest probability. The length of
the longest run of any of these letters is shown to be one greater than
the length of the longest run in a particular state of an associated
Markov chain. Using results of Foulser and Karlin (1987), a conjecture
of a previous paper (Smythe, 2003) concerning the expectation
of this length is verified.
126
60: Probability theory and stochastic processes
On the Complete Convergence ofWeighted Sums for Dependent Random Variables
Fakoor
V.
Azarnoosh
H. A.
1
3
2005
4
1
57
64
22
10
2011
12
09
2015
We study the limiting behavior of weighted sums for
negatively associated (NA) random variables. We extend results in
Wu (1999) and a theorem in Chow and Lai (1973) for NA random
variables.