• Title, Summary, Keyword: shape parameter

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Penalized Likelihood Regression with Negative Binomial Data with Unknown Shape Parameter

  • Kim, Young-Ju
    • Communications for Statistical Applications and Methods
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    • v.14 no.1
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    • pp.23-32
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    • 2007
  • We consider penalized likelihood regression with data from the negative binomial distribution with unknown shape parameter. Smoothing parameter selection and asymptotically efficient low dimensional approximations are employed for negative binomial data along with shape parameter estimation through several different algorithms.

Likelihood Based Inference for the Shape Parameter of the Inverse Gaussian Distribution

  • Lee, Woo-Dong;Kang, Sang-Gil;Kim, Dong-Seok
    • Communications for Statistical Applications and Methods
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    • v.15 no.5
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    • pp.655-666
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    • 2008
  • Small sample likelihood based inference for the shape parameter of the inverse Gaussian distribution is the purpose of this paper. When shape parameter is of interest, the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic are derived. Hsieh (1990) gave a statistical inference for the shape parameter based on an exact method. Throughout simulation, we will compare the statistical properties of the proposed statistics to the statistic given by Hsieh (1990) in term of confidence interval and power of test. We also discuss a real data example.

Asymptotic Inferences on the Shape Parameter of a Gamma Distribution : An Unconditional Approach

  • Na, Jonghwa
    • Journal of the Korean Society for Quality Management
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    • v.22 no.1
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    • pp.162-168
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    • 1994
  • In this paper we develop an unconditional method for inferences on the shape parameter of a gamma distribution. A simple numerical implementation of this unconditional method is developed; this is a computer program that takes the observed data as input and produces the confidence distribution function for the shape parameter, which in turn provides approximate observe significance levels and confidence intervals for that parameter, as output. These approximations are extremely accurate even for very small sample size and numerically simple and easy to obtain.

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Statistical Analysis of Bending-Strength Data of Ceramic Matrix Composites : Estimation of Weibull Shape Parameter (세라믹 복합체의 굽힘강도 데이터의 통계적분석 : 와이블 형상모수의 추정과 비교를 중심으로)

  • 전영록
    • Journal of Applied Reliability
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    • v.1 no.1
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    • pp.17-33
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    • 2001
  • The characteristics of Weibull distribution are investigated as a function of shape parameter. The statistical estimation methods of the shape parameter and statistical comparison methods of two or more shape parameters are studied. Assuming Weibull distribution, statistical analysis of bending-strength data of alumina titanium carbide ceramic matrix composites machined two different methods are performed.

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A Study on the Attribute Analysis of Software Reliability Model with Shape Parameter Change of Infinite Fault NHPP Lomax Life Distribution (무한고장 NHPP Lomax 수명분포의 형상모수 변화에 따른 소프트웨어 신뢰성 모형의 속성 분석에 관한 연구)

  • Min, Kyung-il
    • Journal of Convergence for Information Technology
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    • v.9 no.8
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    • pp.20-26
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    • 2019
  • In this study, the optimal shape parameter condition is presented after analyzing the attributes of the software reliability model according to the change of the shape parameter of Loma life distribution with infinite fault NHPP. In order to analyze the software failure phenomena, the parametric estimation method was applied to the Maximum Likelihood Estimation method, and the nonlinear equation was applied to the bisection method. As a result, it was found that when the attributes according to the change of the shape parameter are compared, the smaller the shape parameter is, the better the prediction ability of the true value, and reliability attributes are efficient. Through this study, it is expected that software developers can increase reliability by preliminarily grasping the type of software failure based on shape parameter, and can be used as basic information to improve the software reliability attributes.

A Study on the Property Analysis of Software Reliability Model with Shape Parameter Change of Finite Fault NHPP Erlang Distribution (유한고장 NHPP 어랑분포의 형상모수 변화에 따른 소프트웨어 신뢰성 모형의 속성 분석에 관한 연구)

  • Min, Kyung Il
    • Journal of Information Technology Applications and Management
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    • v.25 no.4
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    • pp.115-122
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    • 2018
  • Software reliability has the greatest impact on computer system reliability and software quality. For this software reliability analysis, In this study, we compare and analyze the trends of the properties affecting the reliability according to the shape parameters of Erlang distribution based on the finite fault NHPP. Software failure time data were used to analyze software failure phenomena, the maximum likelihood estimation method was used for parameter estimation. As a result, it can be seen that the intensity function is effective because it shows a tendency to decrease with time when the shape parameters a = 1 and a = 3. However, the pattern of the mean value function showed an underestimation pattern for the true values when the shape parameters a = 1 and a = 2, but it was found to be more efficient when a = 3 because the error width from the true value was small. Also, in the reliability evaluation of the future mission time, the stable and high trend was shown when the shape parameters a = 1 and a = 3, but on the contrary, when a = 2, the reliability decreased with the failure time. Through this study, the property of finite fault NHPP Erlang model according to the change of shape parameter without existing research case was newly analyzed, and new research information that software developers can use as basic guideline was presented.

Model Updating of Beams with Shape Change and Measurement Error Using Parameter Modification (파라미터 수정을 사용한 형상변화 및 측정오차가 있는 빔의 모델개선)

  • Yoon, Byung-Ok;Choi, Yoo-Keun;Jang, In-Sik
    • Proceedings of the KSME Conference
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    • pp.335-340
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    • 2001
  • It is important to model the mechanical structure precisely and reasonably in predicting the dynamic characteristics, controlling the vibration, and designing the structure dynamics. In the finite element modeling, the errors can be contained from the physical parameters, the approximation of the boundary conditions, and the element modeling. From the dynamic test, more precise dynamic characteristics can be obtained. Model updating using parameter modification is appropriate when the design parameter is used to analyze the input parameter like finite element method. Finite element analysis for cantilever and simply supported beams with uniform area and shape change are carried out as model updating examples. Mass and stiffness matrices are updated by comparing test and analytical modal frequencies. The result shows that the updated frequencies become closer to the test frequencies.

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Likelihood based inference for the shape parameter of Pareto Distribution

  • Lee, Jae-Un;Lee, Woo-Dong
    • Journal of the Korean Data and Information Science Society
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    • v.19 no.4
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    • pp.1173-1181
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    • 2008
  • In this paper, when the parameter of interest is the shape parameter in Pareto distribution, we develop likelihood based inference for this parameter. Specially, we develop signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic for the shape parameter. It is well-known that as sample size grows, the modified signed log-likelihood ratio statistic converges to standard normal distribution faster than the signed log-likelihood ratio statistic. But the computation of the modified signed log-likelihood statistic is hard or even impossible when the sufficient statistics and the ancillary statistics are not clear. In this case, one can consider an approximation to the modified signed log-likelihood statistic. Specially, when the parameter of interest is informationally orthogonal to the nuisance parameters, we propose the approximate modified signed log-likelihood statistic. Through simulation, we investigate the performances of the proposed statistics with the signed log-likelihood statistic.

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On the Effects of Plotting Positions to the Probability Weighted Moments Method for the Generalized Logistic Distribution

  • Kim, Myung-Suk
    • Communications for Statistical Applications and Methods
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    • v.14 no.3
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    • pp.561-576
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    • 2007
  • Five plotting positions are applied to the computation of probability weighted moments (PWM) on the parameters of the generalized logistic distribution. Over a range of parameter values with some finite sample sizes, the effects of five plotting positions are investigated via Monte Carlo simulation studies. Our simulation results indicate that the Landwehr plotting position frequently tends to document smaller biases than others in the location and scale parameter estimations. On the other hand, the Weibull plotting position often tends to cause larger biases than others. The plotting position (i - 0.35)/n seems to report smaller root mean square errors (RMSE) than other plotting positions in the negative shape parameter estimation under small samples. In comparison to the maximum likelihood (ML) method under the small sample, the PWM do not seem to be better than the ML estimators in the location and scale parameter estimations documenting larger RMSE. However, the PWM outperform the ML estimators in the shape parameter estimation when its magnitude is near zero. Sensitivity of right tail quantile estimation regarding five plotting positions is also examined, but superiority or inferiority of any plotting position is not observed.

The Fractional Bayes Factor Approach to the Bayesian Testing of the Weibull Shape Parameter

  • Cha, Young-Joon;Cho, Kil-Ho;Cho, Jang-Sik
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.3
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    • pp.927-932
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    • 2006
  • The techniques for selecting and evaluating prior distributions are studied over recent years which the primary emphasis is on noninformative priors. But, noninformative priors are typically improper so that such priors are defined only up to arbitrary constants which affect the values of Bayes factors. In this paper, we consider the Bayesian hypotheses testing for the Weibull shape parameter based on fractional Bayes factor which is to remove the arbitrariness of improper priors. Also we present a numerical example to further illustrate our results.

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