• Title/Summary/Keyword: Order Statistics

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Bayesian Prediction Analysis for the Exponential Model Under the Censored Sample with Incomplete Information

  • Kim, Yeung-Hoon;Ko, Jeong-Hwan
    • Journal of the Korean Data and Information Science Society
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    • v.13 no.1
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    • pp.139-145
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    • 2002
  • This paper deals with the problem of obtaining the Bayesian predictive density function and the prediction intervals for a future observation and the p-th order statistics of n future observations for the exponential model under the censored sampling with incomplete information.

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A NOTE ON SOME HIGHER ORDER CUMULANTS IN k PARAMETER NATURAL EXPONENTIAL FAMILY

  • KIM, HYUN CHUL
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.3 no.2
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    • pp.157-160
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    • 1999
  • We show the cumulants of a minimal sufficient statistics in k parameter natural exponential family by parameter function and partial parameter function. We nd the cumulants have some merits of central moments and general cumulants both. The first three cumulants are the central moments themselves and the fourth cumulant has the form related with kurtosis.

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AMLEs for the Exponential Distribution Based on Multiply Type-II Censored Samples

  • Kang Suk-Bok;Lee Sang-Ki
    • Communications for Statistical Applications and Methods
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    • v.12 no.3
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    • pp.603-613
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    • 2005
  • We propose some estimators of the location parameter and derive the approximate maximum likelihood estimators (AMLEs) of the scale parameter in the exponential distribution based on multiply Type-II censored samples. We calculate the moments for the proposed estimators of the location parameter, and the AMLEs which are the linear functions of the order statistics. We compare the proposed estimators in the sense of the mean squared error (MSE) for various censored samples.

Improving Sample Entropy Based on Nonparametric Quantile Estimation

  • Park, Sang-Un;Park, Dong-Ryeon
    • Communications for Statistical Applications and Methods
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    • v.18 no.4
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    • pp.457-465
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    • 2011
  • Sample entropy (Vasicek, 1976) has poor performance, and several nonparametric entropy estimators have been proposed as alternatives. In this paper, we consider a piecewise uniform density function based on quantiles, which enables us to evaluate entropy in each interval, and study the poor performance of the sample entropy in terms of the poor estimation of lower and upper quantiles. Then we propose some improved entropy estimators by simply modifying the quantile estimators, and compare their performances with some existing estimators.

Diagnostics for Regression with Finite-Order Autoregressive Disturbances

  • Lee, Young-Hoon;Jeong, Dong-Bin;Kim, Soon-Kwi
    • Journal of the Korean Statistical Society
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    • v.31 no.2
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    • pp.237-250
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    • 2002
  • Motivated by Cook's (1986) assessment of local influence by investigating the curvature of a surface associated with the overall discrepancy measure, this paper extends this idea to the linear regression model with AR(p) disturbances. Diagnostic for the linear regression models with AR(p) disturbances are discussed when simultaneous perturbations of the response vector are allowed. For the derived criterion, numerical studies demonstrate routine application of this work.

A Study on Error Detection Algorithm of COD Measurement Machine

  • Choi, Hyun-Seok;Song, Gyu-Moon;Kim, Tae-Yoon
    • Journal of the Korean Data and Information Science Society
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    • v.18 no.4
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    • pp.847-857
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    • 2007
  • This paper provides a statistical algorithm which detects COD (chemical oxygen demand) measurement machine error on real-time. For this we propose to use regression model fitting and check its validity against the current observations. The main idea is that the normal regression relation between COD measurement and other parameters inside the machine will be violated when the machine is out of order.

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THE EXPANSION OF MEAN DISTANCE OF BROWNIAN MOTION ON RIEMANNIAN MANIFOLD

  • Kim, Yoon-Tae;Park, Hyun-Suk;Jeon, Jong-Woo
    • Proceedings of the Korean Statistical Society Conference
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    • 2003.05a
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    • pp.37-42
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    • 2003
  • We study the asymptotic expansion in small time of the mean distance of Brownian motion on Riemannian manifolds. We compute the first four terms of the asymptotic expansion of the mean distance by using the decomposition of Laplacian into homogeneous components. This expansion can he expressed in terms of the scalar valued curvature invariants of order 2, 4, 6.

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The Asymptotic Variance of the Studentized Residual Autocorrelations for a Generalized Random Coefficient Autoregressive Processes

  • Park, Sang-Woo;Cho, Sin-Sup;Hwang, Sun Y.
    • Journal of the Korean Statistical Society
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    • v.26 no.4
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    • pp.531-541
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    • 1997
  • The asymptotic distribution of residual autocorrelation functions from a generalized p-order random coefficient autoregressive process (GRCA(p)) is derived. To this end, we first describe the GRCA(p) models and then consider the normalised residuals after fitting the model. This result can be applied to the residual analysis for the diagonostic purpose.

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ARMA Modeling for Nonstationary Time Series Data without Differencing

  • Shin, Dong-Wan;Park, You-Sung
    • Journal of the Korean Statistical Society
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    • v.28 no.3
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    • pp.371-387
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    • 1999
  • For possibly nonstationary autoregressive moving average, modeling based on the original observations rather than the differenced observations is considered. Under this scheme, sample autocorrelation functions, parameter estimates, model diagnostic statistics, and prediction are all computed from the original data instead of the differenced data. The methods and results established under stationarity of data are shown to naturally extend to the nonstationarity of one autoregressive unit root. The sample ACF and PACF can be used for ARMA order determination. The BIC order is strongly consistent. The parameter estimates are asymptotically normal. The portmanteau statistic has chi-square distribution. The predictor is asymptotically equivalent to that based on the differenced data.

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Bayesian Approach to the Prediction in the Censored Sample from Rayleigh Population

  • Ko, Jeong-Hwan;Kim, Young-Hoon;Kang, Sang-Gil
    • Journal of the Korean Data and Information Science Society
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    • v.8 no.1
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    • pp.71-77
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    • 1997
  • S independent sample 0,1,2, $\cdots$, s-1 (or stages 0,1,2, $\cdots$, s-1) are available from the Raleigh population. Procedure for predicting any order statistic in the $(s+1)^{th}$ sample is developed by obtaining the predictive distribution at stage s. Bounds for the sample size at stage S, in order to have the variance at stage S less than that at stage (s-1), are obtained.

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