• Title/Summary/Keyword: Chi Square Statistics

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Bootstrap Inference on the Poisson Rates for Grouped Data

  • Lee, Kee-Won;Kim, Woo-Chul
    • Journal of the Korean Statistical Society
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    • v.30 no.1
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    • pp.1-20
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    • 2001
  • We present how bootstrap methods can be used to conduct inference on the rates of Poisson distributions when only the grouped data are available. A theoretical justification for the validity of bootstrap is given with an illustration of proposed method using a data set obtained fro ma pathology laboratory test. Traditional asymptotic methods are compared with bootstrap methods in computing the estimated standard errors and achieved significance levels for one sample and two sample tests. Bootstrap methods are shown to possess a nice property that he small sample distribution of the relevant statistics can be readily obtained from the bootstrap copies.

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Computational explosion in the frequency estimation of sinusoidal data

  • Zhang, Kaimeng;Ng, Chi Tim;Na, Myunghwan
    • Communications for Statistical Applications and Methods
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    • v.25 no.4
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    • pp.431-442
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    • 2018
  • This paper highlights the computational explosion issues in the autoregressive moving average approach of frequency estimation of sinusoidal data with a large sample size. A new algorithm is proposed to circumvent the computational explosion difficulty in the conditional least-square estimation method. Notice that sinusoidal pattern can be generated by a non-invertible non-stationary autoregressive moving average (ARMA) model. The computational explosion is shown to be closely related to the non-invertibility of the equivalent ARMA model. Simulation studies illustrate the computational explosion phenomenon and show that the proposed algorithm can efficiently overcome computational explosion difficulty. Real data example of sunspot number is provided to illustrate the application of the proposed algorithm to the time series data exhibiting sinusoidal pattern.

Length-biased Rayleigh distribution: reliability analysis, estimation of the parameter, and applications

  • Kayid, M.;Alshingiti, Arwa M.;Aldossary, H.
    • International Journal of Reliability and Applications
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    • v.14 no.1
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    • pp.27-39
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    • 2013
  • In this article, a new model based on the Rayleigh distribution is introduced. This model is useful and practical in physics, reliability, and life testing. The statistical and reliability properties of this model are presented, including moments, the hazard rate, the reversed hazard rate, and mean residual life functions, among others. In addition, it is shown that the distributions of the new model are ordered regarding the strongest likelihood ratio ordering. Four estimating methods, namely, method of moment, maximum likelihood method, Bayes estimation, and uniformly minimum variance unbiased, are used to estimate the parameters of this model. Simulation is used to calculate the estimates and to study their properties. Finally, the appropriateness of this model for real data sets is shown by using the chi-square goodness of fit test and the Kolmogorov-Smirnov statistic.

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A Splog Detection System Using Support Vector Machines and $x^2$ Statistics (지지벡터기계와 카이제곱 통계량을 이용한 스팸 블로그(Splog) 판별 시스템)

  • Lee, Song-Wook
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2010.05a
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    • pp.905-908
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    • 2010
  • Our purpose is to develope the system which detects splogs automatically among blogs on Web environment. After removing HTML of blogs, they are tagged by part of speech(POS) tagger. Words and their POS tags information is used as a feature type. Among features, we select useful features with $x^2$ statistics and train the SVM with the selected features. Our system acquired 90.5% of F1 measure with SPLOG data set.

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Statistical Inference Concerning Local Dependence between Two Multinomial Populations

  • Oh, Myong-Sik
    • Journal of the Korean Data and Information Science Society
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    • v.14 no.2
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    • pp.413-428
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    • 2003
  • If a restriction is imposed only to a (proper) subset of parameters of interest, we call it a local restriction. Statistical inference under a local restriction in multinomial setting is studied. The maximum likelihood estimation under a local restriction and likelihood ratio tests for and against a local restriction are discussed. A real data is analyzed for illustrative purpose.

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Test of Local Restriction on a Multinomial Parameter

  • Oh, Myongsik
    • Communications for Statistical Applications and Methods
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    • v.10 no.2
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    • pp.525-534
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    • 2003
  • If a restriction is imposed only to a (proper) subset of parameters of interest, we call it a local restriction. Statistical inference under a local restriction in multinomial setting is studied. The maximum likelihood estimation under a local restriction and likelihood ratio tests for and against a local restriction are discussed. A real data is analyzed for illustrative purpose.

ON THE GOODNESS OF FIT TEST FOR DISCRETELY OBSERVED SAMPLE FROM DIFFUSION PROCESSES: DIVERGENCE MEASURE APPROACH

  • Lee, Sang-Yeol
    • Journal of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1137-1146
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    • 2010
  • In this paper, we study the divergence based goodness of fit test for partially observed sample from diffusion processes. In order to derive the limiting distribution of the test, we study the asymptotic behavior of the residual empirical process based on the observed sample. It is shown that the residual empirical process converges weakly to a Brownian bridge and the associated phi-divergence test has a chi-square limiting null distribution.

Detection of Random Effects in a Random Effects Model of a One-way Layout Contingency Table

  • Kim, Byung-Soo
    • Journal of the Korean Statistical Society
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    • v.13 no.1
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    • pp.1-19
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    • 1984
  • A random effects model of a one-way layout contingency table is developed using a Dirichlet-multinomial distribution. A test statistic, say $T_k$, is suggested for detecting Dirichlet-multinomial departure from a multinomial distribution. It is shown that the $T_k$ test is asymptotically superior to the classical chi-square test based on the asymptotic relative efficiency. This superiority is further evidenced by a Monte Carlo simulation.

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A dice with 14 faces and its probability assessment (14면 주사위의 확률)

  • 허명회
    • The Korean Journal of Applied Statistics
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    • v.7 no.1
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    • pp.113-119
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    • 1994
  • Logical and frequency probabilities are computed with discussion on their conceptual difference for the case of '14-faces dice' which was excavated in a Unified Silla period pond Anap-chi located at Kyung-ju City, Korea. This wooden dice has eight triangular and six square faces.

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Generalized Kullback-Leibler information and its extensions to censored and discrete cases

  • Park, Sangun
    • Journal of the Korean Data and Information Science Society
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    • v.23 no.6
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    • pp.1223-1229
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    • 2012
  • In this paper, we propose a generalized Kullback-Leibler (KL) information for measuring the distance between two distribution functions where the extension to the censored case is immediate. The generalized KL information has the nonnegativity and characterization properties, and its censored version has the additional property of monotonic increase. We also extend the discussion to the discrete case and propose a generalized censored measure which is comparable to Pearson's chi-square statistic.