• Title/Summary/Keyword: Bivariate distribution

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Other approaches to bivariate ranked set sampling

  • Al-Saleh, Mohammad Fraiwan;Alshboul, Hadeel Mohammad
    • 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.

Nonparametric Estimation of Bivariate Mean Residual Life Function under Univariate Censoring

  • Dong-Myung Jeong;Jae-Kee Song;Joong Kweon Sohn
    • 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.

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Bivariate odd-log-logistic-Weibull regression model for oral health-related quality of life

  • Cruz, Jose N. da;Ortega, Edwin M.M.;Cordeiro, Gauss M.;Suzuki, Adriano K.;Mialhe, Fabio L.
    • Communications for Statistical Applications and Methods
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    • v.24 no.3
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    • pp.271-290
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    • 2017
  • We study a bivariate response regression model with arbitrary marginal distributions and joint distributions using Frank and Clayton's families of copulas. The proposed model is used for fitting dependent bivariate data with explanatory variables using the log-odd log-logistic Weibull distribution. We consider likelihood inferential procedures based on constrained parameters. For different parameter settings and sample sizes, various simulation studies are performed and compared to the performance of the bivariate odd-log-logistic-Weibull regression model. Sensitivity analysis methods (such as local and total influence) are investigated under three perturbation schemes. The methodology is illustrated in a study to assess changes on schoolchildren's oral health-related quality of life (OHRQoL) in a follow-up exam after three years and to evaluate the impact of caries incidence on the OHRQoL of adolescents.

Default Bayesian testing for the bivariate normal correlation coefficient

  • Kang, Sang-Gil;Kim, Dal-Ho;Lee, Woo-Dong
    • Journal of the Korean Data and Information Science Society
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    • v.22 no.5
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    • pp.1007-1016
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    • 2011
  • This article deals with the problem of testing for the correlation coefficient in the bivariate normal distribution. We propose Bayesian hypothesis testing procedures for the bivariate normal correlation coefficient under the noninformative prior. The noninformative priors are usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. A simulation study and an example are provided.

System Reliability from Common Random Stress in a Type II Bivariate Pareto Model with Bivariate Type I Censored Data

  • Cho, Jang-Sik;Choi, Seung-Bae
    • Journal of the Korean Data and Information Science Society
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    • v.15 no.3
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    • pp.655-662
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    • 2004
  • In this paper, we assume that strengths of two components system follow a type II bivariate Pareto model with bivariate type I censored data. And these two components are subjected to a common stress which is independent of the strengths of the components. We obtain estimators for the system reliability based on likelihood function and relative frequency, respectively. Also we construct approximated confidence intervals for the reliability based on maximum likelihood estimator and relative frequency estimator, respectively. Finally we present a numerical study.

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Estimation of the joint conditional distribution for repeatedly measured bivariate cholesterol data using Gaussian copula (가우시안 코플라를 이용한 반복측정 이변량 자료의 조건부 결합 분포 추정)

  • Kwak, Minjung
    • The Korean Journal of Applied Statistics
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    • v.30 no.2
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    • pp.203-213
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    • 2017
  • We study estimation and inference of joint conditional distributions of bivariate longitudinal outcomes using regression models and copulas. We consider a class of time-varying transformation models and combine the two marginal models using Gaussian copulas to estimate the joint models. Our models and estimation method can be applied in many situations where the conditional mean-based models are inadequate. Gaussian copulas combined with time-varying transformation models may allow convenient and easy-to-interpret modeling for the joint conditional distributions for bivariate longitudinal data. We apply our method to an epidemiological study of repeatedly measured bivariate cholesterol data.

ESTIMATING THE CORRELATION COEFFICIENT IN A BIVARIATE NORMAL DISTRIBUTION USING MOVING EXTREME RANKED SET SAMPLING WITH A CONCOMITANT VARIABLE

  • AL-SALEH MOHAMMAD FRAIWAN;AL-ANANBEH AHMAD MOHAMMAD
    • Journal of the Korean Statistical Society
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    • v.34 no.2
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    • pp.125-140
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    • 2005
  • In this paper, we consider the estimation of the correlation coefficient in the bivariate normal distribution, based on a sample obtained using a modification of the moving extreme ranked set sampling technique (MERSS) that was introduced by Al-Saleh and Al-Hadhrami (2003a). The modification involves using a concomitant random variable. Nonparametric-type methods as well as the maximum likelihood estimation are considered under different settings. The obtained estimators are compared to their counterparts that are obtained based simple random sampling (SRS). It appears that the suggested estimators are more efficient

A Comparison of the Efficiency of Location Estimators in Bivariate t distribution

  • Choi, Byong Su;Lee, Seung-Chun
    • Communications for Statistical Applications and Methods
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    • v.10 no.3
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    • pp.895-907
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    • 2003
  • Recent demands for representing the location of multivariate data produce various multivariate medians such as Tukey median, Oja median and spatial median. They are considered as multivariate versions of the median which is widely recognized as a robust alternative to the arithmetic mean. Many studies show that those multivariate median preserve the robustness. However, the effectiveness of those medians is not fully identified. In this note the relative efficiencies of the multivariate medians are investigated in various configurations under the bivariate t-distribution. It is shown that Tukey median outperforms the others in most configurations.

A bivariate extension of the Hosking and Wallis goodness-of-fit measure for regional distributions

  • Kjeldsen, Thomas Rodding;Prosdocimi, Ilaria
    • Proceedings of the Korea Water Resources Association Conference
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    • 2015.05a
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    • pp.239-239
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    • 2015
  • This study presents a bivariate extension of the goodness-of-fit measure for regional frequency distributions developed by Hosking and Wallis [1993] for use with the method of L-moments. Utilising the approximate joint normal distribution of the regional L-skewness and L-kurtosis, a graphical representation of the confidence region on the L-moment diagram can be constructed as an ellipsoid. Candidate distributions can then be accepted where the corresponding the oretical relationship between the L-skewness and L-kurtosis intersects the confidence region, and the chosen distribution would be the one that minimises the Mahalanobis distance measure. Based on a set of Monte Carlo simulations it is demonstrated that the new bivariate measure generally selects the true population distribution more frequently than the original method. An R-code implementation of the method is available for download free-of-charge from the GitHub code depository and will be demonstrated on a case study of annual maximum series of peak flow data from a homogeneous region in Italy.

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Multivariate empirical distribution functions and descriptive methods (다변량 경험분포함수와 시각적인 표현방법)

  • Hong, Chong Sun;Park, Jun;Park, Yong Ho
    • Journal of the Korean Data and Information Science Society
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    • v.28 no.1
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    • pp.87-98
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    • 2017
  • The multivaiate empirical distribution function (MEDF) is defined in this work. The MEDF's expectation and variance are derived and we have shown the MEDF converges to its real distribution function. Based on random samples from bivariate standard normal distribution with various correlation coefficients, we also obtain MEDFs and propose two kinds of graphical methods to visualize MEDFs on two dimensional plane. One is represented with at most n stairs with similar arguments as the step function, and the other is described with at most n curves which look like bivariate quantile vector. Even though these two descriptive methods could be expressed with three dimensional space, two dimensional representation is obtained with ease and it is enough to explain characteristics of bivariate distribution functions. Hence, it is possible to visualize trivariate empirical distribution functions with three dimensional quantile vectors. With bivariate and four variate illustrative examples, the proposed MEDFs descriptive plots are obtained and explored.