• The Korean Journal of Applied Statistics
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• v.25 no.5
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• pp.775-783
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• 2012

Several statistical models for bivariate poisson data are suggested and used to analyze 2011 K-league data. Our interest is composed of two purposes: The first purpose is to exploit potential attacking and defensive abilities of each team. Particular, a bivariate poisson model with diagonal inflation is incorporated for the estimation of draws. A joint model is applied to estimate an association between poisson distribution and probability of draw. The second one is to investigate causes on scoring time of goals and a regression technique of recurrent event data is applied. Some related future works are suggested.

• Journal of the Korean Data and Information Science Society
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• v.18 no.2
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• pp.553-560
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• 2007

In this paper, we consider two components system which lifetimes have Freund's bivariate exponential model with equal failure rates. We propose Bayesian multiple comparisons procedure for the failure rates of I Freund's bivariate exponential populations based on Dirichlet process priors(DPP). The family of DPP is applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through Markov Chain Monte Carlo(MCMC) method, namely, Gibbs sampling, due to the intractability of analytic evaluation. The whole process of multiple comparisons problem for the failure rates of bivariate exponential populations is illustrated through a numerical example.

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.115-123
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• 2012

In animal tumorigenicity data, tumor onsets occur at several sites and onset times cannot be exactly observed. Instead, the existence of tumors is examined only at death time or sacrifice time of the animal. Such an incomplete data structure makes it difficult to investigate the effect of treatment on tumor onset times; in addition, such dependence should be considered when censoring due to death is related with tumor onset. A bivariate frailty effect is incorporated to model bivariate tumor onsets and to connect death with tumor. For the inference of parameters, EM algorithm is applied and a real NTP(National Toxicology Program) dataset is analyzed as an illustrative example.

• Journal of Korean Society for Quality Management
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• v.42 no.1
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• pp.1-14
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• 2014

Purpose: In this paper, the minimal repair-replacement warranty policy is used to carry out a warranty cost analysis with warranty servicing times and failure times that are statistically correlated to bivariate distributions. Methods: Based on the developed approach by Park and Pham (2012a), we investigate the property of the Freund's bivariate exponential distribution and obtain the number of warranty services using the field data to conduct the warranty cost analysis. Results: Maximum likelihood estimates are presented to estimate the parameters and the warranty model is investigated using a Freund's bivariate exponential distribution. A numerical example is discussed to deal with the applicability of the developed approach in the paper. Conclusion: A novel approach of analyzing the warranty cost is proposed for a product in which failure times and warranty servicing times are used simultaneously to investigate the eligibility of a warranty claim.

• International Journal of Reliability and Applications
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• v.13 no.1
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• pp.37-47
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• 2012

In this article we attempted reliability analysis of a component under the stress-strength pattern with both classical as well as Bayesian techniques. The main focus is made to develop the theory for dealing the reliability problems in various circumstances for bivariate environmental set up in context of Bayesian paradigm. A stress-strength based model describes the life of a component which has strength (Y) and is subjected to stress(X). We develop the Bayes and moment estimators of reliability of a component for each of the three possible conditions, under the assumption that the two stresses (i.e. $X_1$ and $X_2$) on a component are dependent and follow a Bivariate exponential (BVE) of Marshall-Olkin distribution, the strength of a component (Y) following exponential distribution is independent of the stresses. The simulation study is performed with Markov Chain Monte Carlo technique via Gibbs sampler to obtain the estimates of Bayes estimators of reliability, are compared with moment estimators of reliabilities on the basis of absolute biases.

• The Korean Journal of Applied Statistics
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• v.22 no.2
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• pp.271-280
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• 2009

For bivariate binomial data with both intra and inter-class correlation, Danaher and Hardie (2005) proposed a bivariate beta-binomial model. However, the model is limited to the situation where the intra-class correlation is strictly positive. Thus it might be seriously inadequate for data with a negative intra-class correlation. Several authors have considered generalized binomial distributions covering a wider range of intra-class correlation which could relax the possible model restrictions imposed. Among others there are the additive/multiplicative and the beta/extended beta binomial model. In this study, bivariate models of the Sarmanov (1966) type are formed by combining each of those univariate models to take care of the inter-class correlation, and are evaluated in terms of the goodness-of-fit. As a result, B-mB and B-ebB are fitted, successfully, to real data and that B-mB, which has a wider permissible range than B-ebB for the intra-class correlation is relatively preferred.

• The Korean Journal of Applied Statistics
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• v.10 no.2
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• pp.293-308
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• 1997

Sliced inverse regression is a method for reducing the dimension of the explanatory variable X without going through any parametric or nonparametric model fitting process. This method explores the simplicity of the inverse view of regression; that is, instead of regressing the univariate output varable y against the multivariate X, we regress X against y. In this article, we propose bivariate sliced inverse regression, whose method regress the multivariate X against the bivariate output variables $y_1, Y_2$. Bivariate sliced inverse regression estimates the e.d.r. directions of satisfying two generalized regression model simultaneously. For the application of bivariate sliced inverse regression, we decompose the output variable y into two variables, one variable y gained by projecting the output variable y onto the column space of X and the other variable r through projecting the output variable y onto the space orthogonal to the column space of X, respectively and then estimate the e.d.r. directions of the generalized regression model by utilize two variables simultaneously. As a result, bivariate sliced inverse regression of considering the variable y and r simultaneously estimates the e.d.r. directions efficiently and steadily when the regression model is linear, quadratic and nonlinear, respectively.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.405-412
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• 2003

In this paper, we consider two components system which the lifetimes have a bivariate weibull distribution with random censored data. Here the censoring time is independent of the lifetimes of the components. We construct large sample tests for independence and symmetry between two-components based on maximum likelihood estimators and the natural estimators. Also we present a numerical study.

• International Journal of Reliability and Applications
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• v.7 no.1
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• pp.55-69
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• 2006

This paper presents a new class of multivariate distributions with Pareto where dependence among the components is characterized by a latent random variable. The new class includes several multivariate and bivariate models of Marshall and Olkin type. It is found the bivariate distribution with Pareto is positively quadrant dependent and its mixture. Some important structural properties of the bivariate distributions with Pareto are discussed. The distribution of minimum in a competing risk Pareto model is derived.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.461-469
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• 2003

In this paper, we consider the series and parallel system which include two components. We assume that the lifetimes of two components follow the bivariate Pareto model with random censored data. We obtain the estimators and approximated confidence intervals of the reliabilities for series and parallel systems based on maximum likelihood estimator and the relative frequency, respectively. Also we present a numerical example by giving a data set which is generated by computer.