• Journal of the Korean Statistical Society
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• v.32 no.4
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• pp.411-423
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• 2003

In this paper we develop a method for calculating a probability that a particular generalized variance is the smallest of all the K multivariate normal generalized variances. The method gives a way of comparing K multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approach for the probability is intractable and thus a Bayesian method is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach. Necessary theory involved in the method and computation is provided.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.73-78
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• 2002

In this paper we develop a method for constructing a Bayesian HPD (highest probability density) interval of a ratio of two multivariate normal generalized variances. The method gives a way of comparing two multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approaches for the interval is intractable and thus a Bayesian HPD(highest probability densith) interval is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach introduced by Chen and Shao(1999). Necessary theory involved in the method and computation is provided.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.477-493
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• 2017

The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random variables like order statistics and lower record values. With this definition we give simple expressions for single and product moments of dual generalized order statistics from Dagum distribution. The results for order statistics and lower records are deduced from the relations derived and some computational works are also carried out. Further, a characterizing result of this distribution on using the conditional moment of the dual generalized order statistics is discussed. These recurrence relations enable computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we tabulate the means, variances, skewness and kurtosis of order statistics and record values of the Dagum distribution.

• Journal of the Korean Statistical Society
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• v.29 no.1
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• pp.45-62
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• 2000

Rotation design is a sampling technique to reduce response burden and to estimate the population characteristics varying in time. Park and Kim(1999) discussed a generation of one-level rotation design which is called as {{{{r_1^m ~-r_2^m-1}}}} design has more applicable form than existing before. In the structure of {{{{r_1^m ~-r_2^m-1}}}} design, we derive the exact variances of generalized composite estimators for level, change and aggregate level characteristics of interest, and optimal coefficients minimizing their variances. Finally numerical examples are shown by the efficiency of alternative designs relative to widely used 4-8-4 rotation design. This is continuous work of Part Ⅰ studied by Park and Kim(1999).

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.295-305
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• 2002

We shall propose several estimators for the shape and scale parameters in a generalized uniform distribution when both parameters are polynomial of a known exposure level, and obtain expectations and variances for their proposed estimators. And we shall compare numerically efficiencies for the several proposed estimators for the shape and scale parameters in a generalized uniform distribution in the small sample sizes.

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.581-587
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• 2010

We shall propose several estimators for the scale parameter in a uniform distri-bution with a generalized uniform outlier when the scale parameter is a function of a known exposure level, and obtain expectations and variances for their proposed estima-tors. And we shall compare numerically efficiencies for proposed estimators of changed parameters of the scale in the small sample sizes.

• Journal of the Korean Data and Information Science Society
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• v.6 no.2
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• pp.77-83
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• 1995

The inferences on a series system under the usual condition using data from constant stress partially accelerated life tests and type I censoring is studied. Two optimal designs to determine the sample proportion allocated each stress level model are also presented, which minimize the sum of the generalized asymptotic variances of maximum likelihood estimators of the failure rate and the acceleration factors and the sum of the asymptotic variances of maximum likelihood estimators of the acceleration factors for each component. Each component of a system is assumed to follow an exponenial distribution.

• Structural Engineering and Mechanics
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• v.47 no.3
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• pp.307-329
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• 2013

The bending problem of Euler-Bernoulli discontinuous beams is dealt with, in which the discontinuities are due to the loads and eventually to essential constrains applied along the beam axis. In particular, the loads are modelled as random delta-correlated processes acting along the beam axis, while the ulterior eventual discontinuities are produced by the presence of external rollers applied along the beam axis. This kind of structural model can be considered in the static study of bridge beams. In the present work the exact expression of the response quantities are given in terms of means and variances, thanks to the use of the stochastic analysis rules and to the use of the generalized functions. The knowledge of the means and the variances of the internal forces implies the possibility of applying the reliability ${\beta}$-method for verifying the beam.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.85-90
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• 2003

In this paper we develop a method for finding optimal ordering of K statistical models. This is based on a dependent paired comparison experimental arrangement whose results can naturally be represented by a completely oriented graph (also so called tournament graph). Introducing preference probabilities, strong transitivity conditions, and an optimal criterion to the graph, we show that a Hamiltonian path obtained from row sum ranking is the optimal ordering. Necessary theories involved in the method and computation are provided. As an application of the method, generalized variances of K multivariate normal populations are compared by a Bayesian approach.

• Journal of the Korean Statistical Society
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• v.21 no.1
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• pp.80-86
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• 1992

The concept of Balanced Factorial Experiment (BFE) was introduced by Shah (1958). The conditions for BFE were set up by Kurkjian and Zelen (1963) and Kshirsagar (1966). Generalized Cyclic Factorial Experiment (GCFE), which is more wide class of designs than BFE, do not satisfy the condition of BFE. So all contrasts belonging to the same interaction are not estimated with equal variance. The main purpose of this paper is to show that GCFE have orthogonal factorial structure and the scheme of the size of variances for all normalized contrasts in GCFE is similar to the original intra-block association scheme.