Maximum Likelihood Estimation in the Weibull Distribution Based On Complete and On Censored Samples

Abstract. The methodology used in wind resource assessments often relies on modeling the wind-speed statistics using a Weibull distribution. In spite of its common use, this distribution has been shown to not always accurately model real wind-speed distributions. Very few studies have examined the arising errors in power outputs, using either observed power productions or theoretical power curves. This article focuses on France, using surface wind measurements at 89 locations covering all regions of the country. It investigates how statistical modeling using a Weibull distribution impacts the prediction of the wind energy content and of the power output in the context of an annual energy production assessment. For this purpose it uses a plausible power curve adapted to each location. Three common methods for fitting the Weibull distribution are tested (maximum likelihood, first and third moments, and the Wind Atlas Analysis and Application Program (WAsP) method). The first two methods generate large errors in the production (mean absolute error around 5 %), especially in the southern areas where the goodness of fit of the Weibull distribution is poorer. The production is mainly overestimated except at some locations with bimodal wind distributions. With the third method, the errors are much lower at most locations (mean absolute error around 2 %). Another distribution, a mixed Rayleigh-Rice distribution, is also tested and shows better skill at assessing the wind energy yield.

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“…-the maximum likelihood estimation (MLE), which maximizes the log likelihood function (Cohen, 1965);…”

Section: Weibull Distributionmentioning

confidence: 99%

Errors in wind resource and energy yield assessments based on the Weibull distribution

Jourdier

Drobinski

2017

Ann. Geophys.

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“…Cohen [5] concluded that the approximate variance covariance matrix may be obtained by replacing expected values by their MLE's. To obtain elements for information matrix, let …”

Section: Approximate Inferencementioning

confidence: 99%

Parameter estimation for multiple weibull populations under joint type-II censoring

Ashour

Eraki

2014

IJASP

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In this paper, we introduce the maximum likelihood estimation for k Weibull populations under joint type II censored scheme and different special cases have been obtained. The asymptotic variance covariance matrix and approximate confidence region based on the asymptotic normality of the maximum likelihood estimators have been obtained. A numerical example is considered to illustrate the proposed estimators.

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“…The asymptotic variance-covariance matrix for 1 2 1 ,,    and 2  can be obtained by inverting the information matrix with the elements that are negative of the expected values of the second order derivatives of logarithms of the likelihood functions. Cohen (1965) concluded that the approximate variance covariance matrix may be obtained by replacing expected values by their MLEs. Now the approximate sample information matrix will be …”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…As the integral in the right side of (9) has no analytical solution, we have to use a numerical technique to solve the integral. According to the invariance property of the MLE, the MLE of the relative risk rates 1  , can be obtained by replacing the MLE of 1 2 1 ,,    and 2  in (9). Based on the above results, When 12 1   , the MLE's of 1  and 2  and the relative risk rates 1  and 2  , corresponds to the results of the exponential distribution obtained by Hemmati and Khorram [11], when the cause of failure is known.…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

Analysis of Generalized Exponential Distribution Under Adaptive Type-II Progressive Hybrid Censored Competing Risks Data

Ashour

Nassar

2014

IJASP

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This paper presents estimates of the parameters based on adaptive type-II progressive hybrid censoring scheme (AT-II PHCS) in the presence of the competing risks model. We consider the competing risks have generalized exponential distributions (GED). The maximum likelihood method is used to derive point and asymptotic confidence intervals for the unknown parameters. The relative risks due to each cause of failure are investigated. A real data set is used to illustrate the theoretical results and to test the hypothesis that the causes of failure follow the generalized exponential distributions against the exponential distribution (ED).

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Maximum Likelihood Estimation in the Weibull Distribution Based On Complete and On Censored Samples

Cited by 461 publications

References 12 publications

Errors in wind resource and energy yield assessments based on the Weibull distribution

Errors in wind resource and energy yield assessments based on the Weibull distribution

Parameter estimation for multiple weibull populations under joint type-II censoring

Analysis of Generalized Exponential Distribution Under Adaptive Type-II Progressive Hybrid Censored Competing Risks Data

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