• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.239-251
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• 2019

In this paper we introduce a new formulation of symmetric homogeneous bivariate means that depends on the variation of a given continuous strictly increasing function on (0, ${\infty}$). It turns out that this class of means includes a lot of known bivariate means among them the arithmetic mean, the harmonic mean, the geometric mean, the logarithmic mean as well as the first and second Seiffert means. Using this new formulation we introduce a lot of new bivariate means and derive some mean-inequalities.

• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.133-144
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• 1996

We, in this paper, propose a nonparametric estimator of bivariate mean residual life function based on Lin and Ying's (1993) bivariate survival function estimator of paired failure times under univariate censoring and prove the uniform consistency and the weak convergence result of this estimator. Through Monte Carlo simulation, the performances of the proposed estimator are tabulated and are illustrated with the skin grafts data.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.45-58
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• 2017

Recently, Sati and Gupta (2015) proposed two measures of uncertainty based on non-extensive entropy, called the dynamic cumulative residual Tsallis entropy (DCRTE) and the empirical cumulative Tsallis entropy. In the present paper, we extend the definition of DCRTE into the bivariate setup and study its properties in the context of reliability theory. We also define a new class of life distributions based on bivariate DCRTE.

• Communications for Statistical Applications and Methods
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• v.23 no.5
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• pp.385-397
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• 2016

The stress-strength models have been intensively investigated in the literature in regards of estimating the reliability ${\theta}$ = P(X > Y) using parametric and nonparametric approaches under different sampling schemes when X and Y are independent random variables. In this paper, we consider the problem of estimating ${\theta}$ when (X, Y) are dependent random variables with a bivariate underlying distribution. The empirical and kernel estimates of ${\theta}$ = P(X > Y), based on bivariate ranked set sampling (BVRSS) are considered, when (X, Y) are paired dependent continuous random variables. The estimators obtained are compared to their counterpart, bivariate simple random sampling (BVSRS), via the bias and mean square error (MSE). We demonstrate that the suggested estimators based on BVRSS are more efficient than those based on BVSRS. A simulation study is conducted to gain insight into the performance of the proposed estimators. A real data example is provided to illustrate the process.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.127-140
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• 2006

AIn this paper we introduce and study a multivariate notions of mean inactivity time (MIT) functions. Basic properties of these functions are derived and their relationship to the multivariate conditional reversed hazard rate functions is studied. A partial ordering, called MIT ordering, of non-negative random vectors is introduced and its basic properties are presented. Its relationship to reversed hazard rate ordering is pointed out. Finally, using the MIT ordering, a bivariate and multivariate notions of IMIT (increasing mean inactivity time) class is introduced and studied.

• Journal of the Korean Statistical Society
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• v.34 no.3
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• pp.245-261
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• 2005

The marginal distribution of X is considered when (X, Y) has a truncated bivariate t-distribution. This paper mainly focuses on the marginal nontruncated distribution of X where Y is truncated below at its mean and its observations are not available. Several properties and applications of this distribution, including relationship with Azzalini's skew-normal distribution, are obtained. To circumvent inferential problem arises from adopting the frequentist's approach, a Bayesian method utilizing a data augmentation method is suggested. Illustrative examples demonstrate the performance of the method.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.921-929
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• 2014

A bivariate exponential distribution with a location parameter is proposed as a model for a two-component shared load system with a guarantee time. Some statistical properties of the proposed model are investigated. The maximum likelihood estimators and uniformly minimum variance unbiased estimators of the parameters, mean time to failure, and the reliability function of system are obtained with unknown guarantee time. Simulation studies are given to illustrate the results.

• Communications for Statistical Applications and Methods
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• v.25 no.3
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• pp.283-296
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• 2018

Ranked set sampling, as introduced by McIntyre (Australian Journal of Agriculture Research, 3, 385-390, 1952), dealt with the estimation of the mean of one population. To deal with two or more variables, different forms of bivariate and multivariate ranked set sampling were suggested. For a technique to be useful, it should be easy to implement in practice. Bivariate ranked set sampling, as introduced by Al-Saleh and Zheng (Australian & New Zealand Journal of Statistics, 44, 221-232, 2002), is not easy to implement in practice, because it requires the judgment ranking of each of the combination of the order statistics of the two characteristics. This paper investigates two modifications that make the method easier to use. The first modification is based on ranking one variable and noting the rank of the other variable for one cycle, and do the reverse for another cycle. The second approach is based on ranking of one variable and giving the second variable the same rank (Concomitant Order Statistic) for one cycle and do the reverse for the other cycle. The two procedures are investigated for an estimation of the means of some well-known distributions. It is show that the suggested approaches can be used in practice and can be more efficient than using SRS. A real data set is used to illustrate the procedure.

• Journal of Korean Society for Quality Management
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• v.18 no.2
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• pp.101-116
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• 1990

The objectives of this thesis are : first, to estimate the parameters and Pr[X < Y] in the Marshall and Olkin's Bivariate Exponential Distribution ; and secondly, to compare the Bayes estimators of Pr[X < Y] with maximum likelihood estimator of Pr[X < Y] in the Marshall and Olkin's Bivariate Exponential Distribution. Through the Monte Carlo Simulation, we observed that the Bayes estimators of Pr[X < Y] perform better than the maximum likelihood estimator of Pr[X < Y] and the Bayes estimator of Pr[X < Y] with gamma prior distribution performs better than with vague prior distribution with respect to bias and mean squared error in the Marshall and Olkin's Bivariate Exponential Distribution.

• Water for future
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• v.12 no.2
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• pp.63-69
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• 1979

The sequences of monthly streamflows constitute a non-statonary time series. The purely stochastic model has been applied to data generation of non-stationary time series. Tow different mothods--single site and multisite generation--have been used on the hydrologic time series. In this study the synthetic generation method by bivariate analysis, studied by Thomas Fiering, one of multi-site models, has been applied to the historical data on monthly streamflows at two sites in Nakdong River, and also for validity of this model the single site Thomas Fiering model applied. Through statistical analysis it has been shown that the performance of bivariate Thomas Fiering model was better than that of the other. By comparison of mean and standard deviaion between the historical and the generated, and cross correlogram interpretation, it has been known that the model used herein has good performance to simultaneously generate the monthly streamflows at two sites in a river hasin.