Sufficient conditions for stochastic equality of two distributions under some partial orders

2010 ◽  
Vol 80 (5-6) ◽  
pp. 513-518
Author(s):  
B.L.S. Prakasa Rao ◽  
Harshinder Singh
Keyword(s):  
Sufficient Conditions ◽  
Partial Orders ◽  
Stochastic Equality

scholarly journals Extensions of strict partial orders in N-Groups

1978 ◽  
Vol 25 (2) ◽  
pp. 241-249 ◽  
Author(s):  
K. B. Prabhakara Rao
Keyword(s):  
Partial Order ◽  
Sufficient Conditions ◽  
Partial Orders ◽  
Necessary And Sufficient Conditions ◽  
Full Extension ◽  
Partially Ordered ◽  
Strict Partial Order ◽  
Positive Elements ◽  
Necessary And Sufficient

AbstractAn attempt is made to extend the theory of extensions of partial orders in groups to strict partially ordered N-groups. Necessary and sufficient conditions, for a strict partial order of an N-group to have a strict full extension, and for a strict partial order of an N-group to be an intersection of strict full orders, are obtained when the partially ordered near-ring N and the N-group G satisfy the condition (− x) n = − xn for all elements x in G and positive elements n in N.

Sufficient conditions for Lorenz ordering with common finite support

2021 ◽  
pp. 1-7
Author(s):  
Barry Arnold
Keyword(s):  
Sufficient Conditions ◽  
Partial Orders ◽  
Finite Support ◽  
Lorenz Order ◽  
The Common

Arnold and Gokhale (2017) provided a characterization of the Lorenz inequality order between distributions with common finite support. In the more general Lorenz order context, a variety of partial orders are often used to verify the existence of Lorenz ordering. In this paper we investigate whether parallel results can be identified within the common finite support context.

Multivariate Convex Orderings, Dependence, and Stochastic Equality

1998 ◽  
Vol 35 (1) ◽  
pp. 93-103 ◽  
Author(s):  
Marco Scarsini
Keyword(s):  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Multivariate Normal ◽  
Random Vectors ◽  
Linear Combinations ◽  
Convex Ordering ◽  
Normal Distributions ◽  
Necessary And Sufficient ◽  
Stochastic Equality

We consider the convex ordering for random vectors and some weaker versions of it, like the convex ordering for linear combinations of random variables. First we establish conditions of stochastic equality for random vectors that are ordered by one of the convex orderings. Then we establish necessary and sufficient conditions for the convex ordering to hold in the case of multivariate normal distributions and sufficient conditions for the positive linear convex ordering (without the restriction to multi-normality).

Multivariate Convex Orderings, Dependence, and Stochastic Equality

1998 ◽  
Vol 35 (01) ◽  
pp. 93-103 ◽  
Author(s):  
Marco Scarsini
Keyword(s):  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Multivariate Normal ◽  
Random Vectors ◽  
Linear Combinations ◽  
Convex Ordering ◽  
Normal Distributions ◽  
Necessary And Sufficient ◽  
Stochastic Equality

We consider the convex ordering for random vectors and some weaker versions of it, like the convex ordering for linear combinations of random variables. First we establish conditions of stochastic equality for random vectors that are ordered by one of the convex orderings. Then we establish necessary and sufficient conditions for the convex ordering to hold in the case of multivariate normal distributions and sufficient conditions for the positive linear convex ordering (without the restriction to multi-normality).

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

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