Some sufficient conditions for the E- and MV-optimality of block designs having blocks of unequal size

1987 ◽  
Vol 39 (2) ◽  
pp. 385-397 ◽  
Author(s):  
K. Y. Lee ◽  
Mike Jacroux
Keyword(s):  
Sufficient Conditions ◽  
Block Designs ◽  
Unequal Size

Designs Robust Against Aberrations

1993 ◽  
Vol 43 (1-2) ◽  
pp. 95-108 ◽  
Author(s):  
N. K. Mandal ◽  
K. R. Shah
Keyword(s):  
Sufficient Conditions ◽  
Subject Classification ◽  
Alternative Formulation ◽  
Block Designs ◽  
Ams Subject Classification ◽  
Secondary 62K05

In this paper, we obtain sufficient conditions for a design to be robust against aberrations in the sense of Box and Draper. Block designs, row-column designs and fractional designs are considered here. An alternative formulation of robustness is also presented. AMS Subject Classification: Primary 62K99; Secondary 62K05.

scholarly journals A Regular D‑optimal Weighing Design with Negative Correlations of Errors

2019 ◽  
Vol 5 (344) ◽  
pp. 7-16
Author(s):  
Małgorzata Graczyk ◽  
Bronisław Ceranka
Keyword(s):  
Sufficient Conditions ◽  
Optimal Estimation ◽  
Block Designs ◽  
Correlated Errors ◽  
Unknown Parameters ◽  
Chemical Balance ◽  
Construction Methods ◽  
New Construction ◽  
Balanced Incomplete Block ◽  
Necessary And Sufficient

The issues concerning optimal estimation of unknown parameters in the model of chemical balance weighing designs with negative correlated errors are considered. The necessary and sufficient conditions determining the regular D‑optimal design and some new construction methods are presented. They are based on the incidence matrices of balanced incomplete block designs and balanced bipartite weighing designs.  

scholarly journals Highly D‑efficient Weighing Design and Its Construction

2018 ◽  
Vol 5 (331) ◽  
pp. 143-151
Author(s):  
Bronisław Ceranka ◽  
Małgorzata Graczyk
Keyword(s):  
Sufficient Conditions ◽  
Block Designs ◽  
Incidence Matrices ◽  
Balanced Incomplete Block Designs ◽  
Construction Methods ◽  
Design Optimality ◽  
Spring Balance ◽  
New Construction ◽  
Balanced Incomplete Block ◽  
Necessary And Sufficient

In this paper, some aspects of design optimality on the basis of spring balance weighing designs are considered. The properties of D‑optimal and D‑efficiency designs are studied. The necessary and sufficient conditions determining the mentioned designs and some new construction methods are introduced. The methods of determining designs that have the required properties are based on a set of incidence matrices of balanced incomplete block designs and group divisible designs.

scholarly journals A-optimal chemical balance weighing design under certain condition

2007 ◽  
Vol 4 (1) ◽  
Author(s):  
Bronisław Ceranka ◽  
Małgorzata Graczyk
Keyword(s):  
Lower Bound ◽  
Sufficient Conditions ◽  
Design Matrix ◽  
Block Designs ◽  
Chemical Balance ◽  
Incidence Matrices ◽  
Construction Methods ◽  
New Construction ◽  
The Right ◽  
Necessary And Sufficient

The paper is studying the estimation problem of individual weights of \(p\) objects using the design matrix \(\mathbf{X}\) of the A-optimal chemical balance weighing design under the restriction \(p_1 + p_2 = q  \leq p\), where \(p_1\) and \(p_2\) represent the number of objects placed on the left pan and on the right pan, respectively, in each of the measurement operations. The lower bound of \(\mathrm{Tr}(\mathbf{X}^{\prime}\mathbf{X})^{-1}\) is attained and the necessary and sufficient conditions for this lower bound to be obtained are given. There are given new construction methods of the A-optimal chemical balance weighing designs based on incidence matrices of the balanced bipartite weighing designs and the ternary balanced block designs.

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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