• Title/Summary/Keyword: Weibull distribution

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A Weibull Model Building Technique for Reliability Assessment with Limited failure Data (신뢰도 평가에서 제한된 데이터를 이용한 와이블분포 모형화 기법)

  • Kim, Gwang-Won
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.55 no.3
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    • pp.109-115
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    • 2006
  • The Weibull distribution is a good candidate for accurate probabilistic model with its rich shape-forming ability and relatively simple CDF(cumulative distribution function). If there are sufficient information to get convincible mean and variance for a probabilistic event, reliable parameters of the Weibull distribution can be determined uniquely. However, sufficient information is not given as usual. There needs more deliberate model building method for that case. This Paper presents an effective parameter estimation technique for Weibull distribution with limited failure data.

ON CHARACTERIZATIONS OF THE WEIBULL DISTRIBUTION BY THE INDEPENDENT PROPERTY OF RECORD VALUES

  • Lee, Min-Young;Lim, Eun-Hyuk
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.2
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    • pp.245-250
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    • 2010
  • We present characterizations of the Weibull distribution by the independent property of record values that F(x) has a Weibull distribution if and only if $\frac{X_{U(m)}}{X_{U(n)}}$ and $X_{U(n)}$ or $\frac{X_{U(n)}}{X_{U(n)}{\pm}X_{U(m)}}$ and $X_{U(n)}$ are independent for $1{\leq}m.

Comparative Analysis of Flood Frequncy by Moment and L-moment in Weibull-3 distribution (Weibull-3 분포모형의 모멘트법 및 L-모멘트법에 의한 홍수빈도비교분석)

  • 이순혁;맹승진;송기헌;류경식;지호근
    • Proceedings of the Korean Society of Agricultural Engineers Conference
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    • 1998.10a
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    • pp.331-337
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    • 1998
  • This study was carried out to derive optimal design floods by Weibull-3 distribution with the annual maximum series at seven watersheds along Man, Nagdong, Geum, Yeongsan and Seomjin river systems. Adequacy for the analysis of flood data used in this study was acknowledged by the tests of Independence, Homogeneity, detection of Outliers. Parameters were estimated by the Methods of Moments and L-Moments. Design floods obtained by Methods of Moments and L-Moments using different methods for plotting positions in Weibull-3 distribution were compared by the rotative mean error and relative absolute error. It has shown that design floods derived by the method of L-moments using Weibull plotting position formula in Weibull-3 distribution are much closer to those of the observed data in comparison with those obtained by method of moments using different formulas for plotting positions in view of relative mean and relative absolute error.

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Mathematical representation to assess the wind resource by three parameter Weibull distribution

  • Sukkiramathi, K.;Rajkumar, R.;Seshaiah, C.V.
    • Wind and Structures
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    • v.31 no.5
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    • pp.419-430
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    • 2020
  • Weibull distribution is a conspicuous distribution known for its accuracy and its usage for wind energy analysis. The two and three parameter Weibull distributions are adopted in this study to fit wind speed data. The daily mean wind speed data of Ennore, Tamil Nadu, India has been used to validate the procedure. The parameters are estimated using maximum likelihood method, least square method and moment method. Four statistical tests namely Root mean square error, R2 test, Kolmogorov-Smirnov test and Anderson-Darling test are employed to inspect the fitness of Weibull probability density functions. The value of shape factor, scale factor, wind speed and wind power are determined at a height of 100m using extrapolation of numerical equations. Also, the value of capacity factor is calculated mathematically. This study provides a way to evaluate feasible locations for wind energy assessment, which can be used at any windy site throughout the world.

An alternative approach to extreme value analysis for design purposes

  • Bardsley, Earl
    • Proceedings of the Korea Water Resources Association Conference
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    • 2016.05a
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    • pp.201-201
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    • 2016
  • The asymptotic extreme value distributions of maxima are a natural choice when designing against future extreme events like flood peaks or wave heights, given a stationary time series. The generalized extreme value distribution (GEV) is often utilised in this context because it is seen as a convenient single expression for extreme event analysis. However, the GEV has a drawback because the location of the distribution bound relative to the data is a discontinuous function of the GEV shape parameter. That is, for annual maxima approximated by the Gumbel distribution, the data is also consistent with a GEV distribution with an upper bound (no lower bound) or a GEV distribution with a lower bound (no upper bound). A more consistent single extreme value expression for design purposes is proposed as the Weibull distribution of smallest extremes, as applied to transformed annual maxima. The Weibull distribution limit holds here for sufficiently large sample sizes, irrespective of the extreme value domain of attraction applicable to the untransformed maxima. The Gumbel, Type 2, and Type 3 extreme value distributions thus become redundant, together with the GEV, because in reality there is only a single asymptotic extreme value distribution required for design purposes - the Weibull distribution of minima as applied to transformed maxima. An illustrative synthetic example is given showing transformed maxima from the normal distribution approaching the Weibull limit much faster than the untransformed sample maxima approach the normal distribution Gumbel limit. Some New Zealand examples are given with the Weibull distribution being applied to reciprocal transformations of annual flood maxima, where the untransformed maxima follow apparently different extreme value distributions.

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Some Exponentiated Distributions

  • Ali, M. Masoom;Pal, Manisha;Woo, Jung-Soo
    • Communications for Statistical Applications and Methods
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    • v.14 no.1
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    • pp.93-109
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    • 2007
  • In this paper we study a number of new exponentiated distributions. The survival function, failure rate and moments of the distributions have been derived using certain special functions. The behavior of the failure rate has also been studied.

Bayesian Estimators Using Record Statistics of Exponentiated Inverse Weibull Distribution

  • Kim, Yong-Ku;Seo, Jung-In;Kang, Suk-Bok
    • Communications for Statistical Applications and Methods
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    • v.19 no.3
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    • pp.479-493
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    • 2012
  • The inverse Weibull distribution(IWD) is a complementary Weibull distribution and plays an important role in many application areas. In this paper, we develop a Bayesian estimator in the context of record statistics values from the exponentiated inverse Weibull distribution(EIWD). We obtained Bayesian estimators through the squared error loss function (quadratic loss) and LINEX loss function. This is done with respect to the conjugate priors for shape and scale parameters. The results may be of interest especially when only record values are stored.

Nonparametric Bayesian estimation on the exponentiated inverse Weibull distribution with record values

  • Seo, Jung In;Kim, Yongku
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.3
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    • pp.611-622
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    • 2014
  • The inverse Weibull distribution (IWD) is the complementary Weibull distribution and plays an important role in many application areas. In Bayesian analysis, Soland's method can be considered to avoid computational complexities. One limitation of this approach is that parameters of interest are restricted to a finite number of values. This paper introduce nonparametric Bayesian estimator in the context of record statistics values from the exponentiated inverse Weibull distribution (EIWD). In stead of Soland's conjugate piror, stick-breaking prior is considered and the corresponding Bayesian estimators under the squared error loss function (quadratic loss) and LINEX loss function are obtained and compared with other estimators. The results may be of interest especially when only record values are stored.