• Title, Summary, Keyword: Weibull distribution

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Notes on a skew-symmetric inverse double Weibull distribution

  • Woo, Jung-Soo
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.2
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    • pp.459-465
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    • 2009
  • For an inverse double Weibull distribution which is symmetric about zero, we obtain distribution and moment of ratio of independent inverse double Weibull variables, and also obtain the cumulative distribution function and moment of a skew-symmetric inverse double Weibull distribution. And we introduce a skew-symmetric inverse double Weibull generated by a double Weibull distribution.

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Inverted exponentiated Weibull distribution with applications to lifetime data

  • Lee, Seunghyung;Noh, Yunhwan;Chung, Younshik
    • Communications for Statistical Applications and Methods
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    • v.24 no.3
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    • pp.227-240
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    • 2017
  • In this paper, we introduce the inverted exponentiated Weibull (IEW) distribution which contains exponentiated inverted Weibull distribution, inverse Weibull (IW) distribution, and inverted exponentiated distribution as submodels. The proposed distribution is obtained by the inverse form of the exponentiated Weibull distribution. In particular, we explain that the proposed distribution can be interpreted by Marshall and Olkin's book (Lifetime Distributions: Structure of Non-parametric, Semiparametric, and Parametric Families, 2007, Springer) idea. We derive the cumulative distribution function and hazard function and calculate expression for its moment. The hazard function of the IEW distribution can be decreasing, increasing or bathtub-shaped. The maximum likelihood estimation (MLE) is obtained. Then we show the existence and uniqueness of MLE. We can also obtain the Bayesian estimation by using the Gibbs sampler with the Metropolis-Hastings algorithm. We also give applications with a simulated data set and two real data set to show the flexibility of the IEW distribution. Finally, conclusions are mentioned.

Estimations in a Skewed Double Weibull Distribution

  • Son, Hee-Ju;Woo, Jung-Soo
    • Communications for Statistical Applications and Methods
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    • v.16 no.5
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    • pp.859-870
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    • 2009
  • We obtain a skewed double Weibull distribution by a double Weibull distribution, and evaluate its coefficient of skewness. And we obtain the approximate maximum likelihood estimator(AML) and moment estimator of skew parameter in the skewed double Weibull distribution, and hence compare simulated mean squared errors(MSE) of those estimators. We compare simulated MSE of two proposed reliability estimators in two independent skewed double Weibull distributions each with different skew parameters. Finally we introduce a skewed double Weibull distribution generated by a uniform kernel.

A new flexible Weibull distribution

  • Park, Sangun;Park, Jihwan;Choi, Youngsik
    • Communications for Statistical Applications and Methods
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    • v.23 no.5
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    • pp.399-409
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    • 2016
  • Many of studies have suggested the modifications on Weibull distribution to model the non-monotone hazards. In this paper, we combine two cumulative hazard functions and propose a new modified Weibull distribution function. The newly suggested distribution will be named as a new flexible Weibull distribution. Corresponding hazard function of the proposed distribution shows flexible (monotone or non-monotone) shapes. We study the characteristics of the proposed distribution that includes ageing behavior, moment, and order statistic. We also discuss an estimation method for its parameters. The performance of the proposed distribution is compared with existing modified Weibull distributions using various types of hazard functions. We also use real data example to illustrate the efficiency of the proposed distribution.

The Exponentiated Weibull-Geometric Distribution: Properties and Estimations

  • Chung, Younshik;Kang, Yongbeen
    • Communications for Statistical Applications and Methods
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    • v.21 no.2
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    • pp.147-160
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    • 2014
  • In this paper, we introduce the exponentiated Weibull-geometric (EWG) distribution which generalizes two-parameter exponentiated Weibull (EW) distribution introduced by Mudholkar et al. (1995). This proposed distribution is obtained by compounding the exponentiated Weibull with geometric distribution. We derive its cumulative distribution function (CDF), hazard function and the density of the order statistics and calculate expressions for its moments and the moments of the order statistics. The hazard function of the EWG distribution can be decreasing, increasing or bathtub-shaped among others. Also, we give expressions for the Renyi and Shannon entropies. The maximum likelihood estimation is obtained by using EM-algorithm (Dempster et al., 1977; McLachlan and Krishnan, 1997). We can obtain the Bayesian estimation by using Gibbs sampler with Metropolis-Hastings algorithm. Also, we give application with real data set to show the flexibility of the EWG distribution. Finally, summary and discussion are mentioned.

Approximated Modeling Technique of Weibull Distributed Radar Clutter (Weibull 분포 레이더 클러터의 근사적 모델링 기법)

  • Nam, Chang-Ho;Ra, Sung-Woong
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.23 no.7
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    • pp.822-830
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    • 2012
  • Clutters are all unwanted radar returns to affect on detection of targets. Radar clutter is characterized by amplitude distributions, spectrum, etc. Clutter is modelled with considering these kinds of characteristics. In this paper, a Weibull distribution function approximated by uniform distribution function is suggested. Weibull distribution function is used to model the various clutters. This paper shows that the data generated by the approximated solution of Weibull distribution function satisfy the Weibull probability density function. This paper shows that the data generation time of approximated Weibull distribution function solution is reduced by 20 % compared with the generation time of original Weibull probability density function.

Failure Rate Calculation using the Mixture Weibull Distribution (혼합 와이블 분포를 이용한 고장률 산출 기법에 관한 연구)

  • Chai, Hui-seok;Shin, Joong-woo;Lim, Tae-jin;Kim, Jae-chul
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.66 no.3
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    • pp.500-506
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    • 2017
  • In 2014, ISO 55000s has been enacted and the power plant asset management is becoming a hot issue for all over the world. The asset management system is being developed as a combination of CBM(Condition Based Maintenance) and RCM(Reliability Centered Maintenance). Therefore, the research on the calculation of the failure rate which is the most basic index of RCM is actively carried out. The failure rate calculation has been going on for a long time, and the most widely used probability distribution is the Weibull distribution. In the Weibull distribution, the failure rate function is determined in three types according to the value of the shape parameter. However, the Weibull distribution has a limitation that it is difficult to apply it when the trend of failure rate changes-such as bathtub curves. In this paper, the failure rate is calculated using the mixture Weibull distribution which can appropriately express the change of the shape of the failure rate. Based on these results, we propose the necessity and validity of applying mixture Weibull distribution.

Mathematical modeling of wind power estimation using multiple parameter Weibull distribution

  • Chalamcharla, Seshaiah C.V.;Doraiswamy, Indhumathy D.
    • Wind and Structures
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    • v.23 no.4
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    • pp.351-366
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    • 2016
  • Nowadays, wind energy is the most rapidly developing technology and energy source and it is reusable. Due to its cleanliness and reusability, there have been rapid developments made on transferring the wind energy systems to electric energy systems. Converting the wind energy to electrical energy can be done only with the wind turbines. So installing a wind turbine depends on the wind speed at that location. The expected wind power can be estimated using a perfect probability distribution. In this paper Weibull and Weibull distribution with multiple parameters has been used in deriving the mathematical expression for estimating the wind power. Statistically the parameters of Weibull and Weibull distribution are estimated using the maximum likelihood techniques. We derive a probability distribution for the power output of a wind turbine with given rated wind speeds for the regions where the wind speed histograms present a bimodal pdf and compute the first order moment of this distribution.

A Probabilistic Analysis on Fracture Strength of Ceramics (세라믹스의 파괴강도에 관한 확률론적 해석)

  • 김선진
    • Journal of Ocean Engineering and Technology
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    • v.10 no.2
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    • pp.61-68
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    • 1996
  • Weibull distribution function is applied very successfully to the strength of brittle materials such as ceramics and the weakest link model is applied to explain the ovents. This paper deals with the effect of specimen size on the strength of ceramics. The values of tensile strength were calculated by the Monte-Calro simuation. The tensile strength obtained was plotted on Weibull probabillity papers and represented by the 3-parameter Weibull distribution. The strength distribution function was compared with the theoretical weibull distribution. As a result, it was found that the Weibull shape parameter was changed due to the size and there was a possibility of a false indication as if the weakest link model holds good. We should be very careful when we apply the Weibull statistics to estimate the strength of products.

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