• 제목/요약/키워드: Maximum likelihood estimates

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Parameter estimation of an extended inverse power Lomax distribution with Type I right censored data

  • Hassan, Amal S.;Nassr, Said G.
    • Communications for Statistical Applications and Methods
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    • 제28권2호
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    • pp.99-118
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    • 2021
  • In this paper, we introduce an extended form of the inverse power Lomax model via Marshall-Olkin approach. We call it the Marshall-Olkin inverse power Lomax (MOIPL) distribution. The four- parameter MOIPL distribution is very flexible which contains some former and new models. Vital properties of the MOIPL distribution are affirmed. Maximum likelihood estimators and approximate confidence intervals are considered under Type I censored samples. Maximum likelihood estimates are evaluated according to simulation study. Bayesian estimators as well as Bayesian credible intervals under symmetric loss function are obtained via Markov chain Monte Carlo (MCMC) approach. Finally, the flexibility of the new model is analyzed by means of two real data sets. It is found that the MOIPL model provides closer fits than some other models based on the selected criteria.

단계별로 얻어진 이차원 분할표의 모수 추정을 위한 정확최대우도추정법과 단계별추출추정법의 비교 (Comparison of Step-Wise and Exact Maximum Likelihood Estimations on Cell Probabilities of Contingency Table)

  • 이상은;강기훈;정석오;신기일
    • Communications for Statistical Applications and Methods
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    • 제17권1호
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    • pp.67-77
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    • 2010
  • 단계별로 얻어진 $I{\times}J$ 이차원 범주형 자료에서 분할표 일부의 칸에서 도수가 붕괴(collapse)된 상태로 조사가 이루어진 것을 단계별추출(step-wise sampling)이라 한다. 단계별추출로 얻어진 자료를 분석할 경우 단계별추출법을 사용하여 분석하면 분석의 효과를 얻을 수 있다. 본 논문에서는 단계별추출법 중에서 최대우도추정법을 이용하여 얻어진 정확최대우도추정량(exact maximum likelihood estimator)과 단계별추출최대우도추정량을 연구하였다. 또한 MSE와 편향(bias)을 기준으로 모의실험을 통하여 두 추정법을 비교하였다.

Semiparametric Inference for a Multistate Stochastic Survival Model

  • Sung Chil Yeo
    • Communications for Statistical Applications and Methods
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    • 제5권1호
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    • pp.239-263
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    • 1998
  • In this paper, we consider a multistate survival model which incorporates covariates and contains two illness states and two death states. The underlying stochastic process is assumed to follow nonhomogeneous Markov process. The estimates of survival, transition and competing risks probabilities are given via the methods of partial likelihood and nonparametric maximum likelihood. Our discussion is based on the statistical theory of counting process. An illustration is given to the data of patients in a heart transplant program. The goodness of fit procedures are also discussed to check the adequacy of the model.

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ORDER RESTRICTED TESTS FOR SYMMETRY AGAINST POSITIVE BIASEDNESS

  • Oh, Myong-Sik
    • Journal of the Korean Statistical Society
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    • 제36권3호
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    • pp.335-347
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    • 2007
  • Two new types of positive biasedness, which are closely related to Type III positive biasedness (Yanagimoto and Sibuya, 1972), are proposed. We call these near Type III positive biasedness. Though no implication between Type II and near Type III biasedness exists, near Type III seems to be less restrictive than Type II biasedness. Constrained maximum likelihood estimates of distribution functions under near Type III positive bisedness are obtained. The likelihood ratio tests of symmetry against new positive biasedness restrictions are proposed. A small simulation study is conducted to compare the performance of the tests.

Some Computational Contribution on the Estimation Procedure of a First Order Moving Average

  • Kim, Dai-Young
    • Journal of the Korean Statistical Society
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    • 제2권1호
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    • pp.9-15
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    • 1973
  • In the first-order moving average model, we present the exact likelihood equations as function of variance, correlation and parameters of coefficients in the orthogonally transformed model. Existence of maximum likelihood estimates for these unknowns are studied and a computational method is provided. (Because of the limited space Ive do not present the computer program which is written in FORTRAN.) 40 sets of generated data and economic data are used to demonstrate, and few of them are presented in the Appendix. A numerical comparison of MLE with the efficient estimate proposed by Durbin is presented in the particular case.

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질병의 범주적 자료에 대한 통계적 분석모형 (A generalized model for categorical data from epidemiological studies)

  • 최재성
    • 응용통계연구
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    • 제9권1호
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    • pp.1-15
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    • 1996
  • 본 논문은 질병발생집단의 감염율이 질병발생집단내 감염되지 않은 개체들에 대한 어떤 처치효과가 감염율에 어떻게 영향을 받는가를 알아보기 위한 통계적 분석모형으로 연속적 분석모형을 제시하고, 모형내 미지모수들을 추정하기 위한 방법을 논의하고 있다.

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Statistical Inference Concerning Peakedness Ordering between Two Symmetric Distributions

  • Oh, Myong-Sik
    • Journal of the Korean Data and Information Science Society
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    • 제15권1호
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    • pp.201-210
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    • 2004
  • The peakedness ordering is closely related to dispersive ordering. In this paper we consider the statistical inference concerning peakedness ordering between two arbitrary symmetric distributions. Nonparametric maximum likelihood estimates of two distribution functions under symmetry and peakedness ordering are given. The likelihood ratio test for equality of two symmetric discrete distributions in the sense of peakedness ordering is studied.

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Partitioning likelihood method in the analysis of non-monotone missing data

  • Kim Jae-Kwang
    • 한국통계학회:학술대회논문집
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    • 한국통계학회 2004년도 학술발표논문집
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    • pp.1-8
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    • 2004
  • We address the problem of parameter estimation in multivariate distributions under ignorable non-monotone missing data. The factoring likelihood method for monotone missing data, termed by Robin (1974), is extended to a more general case of non-monotone missing data. The proposed method is algebraically equivalent to the Newton-Raphson method for the observed likelihood, but avoids the burden of computing the first and the second partial derivatives of the observed likelihood Instead, the maximum likelihood estimates and their information matrices for each partition of the data set are computed separately and combined naturally using the generalized least squares method. A numerical example is also presented to illustrate the method.

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Different estimation methods for the unit inverse exponentiated weibull distribution

  • Amal S Hassan;Reem S Alharbi
    • Communications for Statistical Applications and Methods
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    • 제30권2호
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    • pp.191-213
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    • 2023
  • Unit distributions are frequently used in probability theory and statistics to depict meaningful variables having values between zero and one. Using convenient transformation, the unit inverse exponentiated weibull (UIEW) distribution, which is equally useful for modelling data on the unit interval, is proposed in this study. Quantile function, moments, incomplete moments, uncertainty measures, stochastic ordering, and stress-strength reliability are among the statistical properties provided for this distribution. To estimate the parameters associated to the recommended distribution, well-known estimation techniques including maximum likelihood, maximum product of spacings, least squares, weighted least squares, Cramer von Mises, Anderson-Darling, and Bayesian are utilised. Using simulated data, we compare how well the various estimators perform. According to the simulated outputs, the maximum product of spacing estimates has lower values of accuracy measures than alternative estimates in majority of situations. For two real datasets, the proposed model outperforms the beta, Kumaraswamy, unit Gompartz, unit Lomax and complementary unit weibull distributions based on various comparative indicators.

불균등 구간검사를 이용한 지수수명시간의 추정 (Exponential Lifetime Estimation with Unequal Interval Censoring)

  • 이태섭;윤상운
    • 한국신뢰성학회지:신뢰성응용연구
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    • 제2권2호
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    • pp.113-119
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    • 2002
  • The estimation of mean lifetimes in presence of interval censoring with replacement procedure are examined when the distributions of lifetimes are exponential. It is assumed that, due to physical restrictions and/or economic constraints, the number of failures is investigated only at several inspection times during the lifetime test. The maximum likelihood estimator is found in an implicit form. The Cramer-Rao lower bounds of the estimates are found in places of variances and by simulations the properties of the estimates are examined.

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