Relevant bibliographies by topics / Weibull distribution function

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Academic literature on the topic 'Weibull distribution function'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Weibull distribution function"

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Oluyede, Broderick. "The Gamma-Weibull-G Family of Distributions with Applications." Austrian Journal of Statistics 47, no. 1 (January 30, 2018): 45–76. http://dx.doi.org/10.17713/ajs.v47i1.155.

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Weibull distribution and its extended families has been widely studied in lifetime applications. Based on the Weibull-G family of distributions and the exponentiated Weibull distribution, we study in detail this new class of distributions, namely, Gamma-WeibullG family of distributions (GWG). Some special models in the new class are discussed. Statistical properties of the family of distributions, such as expansion of density function, hazard and reverse hazard functions, quantile function, moments, incomplete moments, generating functions, mean deviations, Bonferroni and Lorenz curves and order statistics are presented. We also present R´enyi entropy, estimation of parameters by using method of maximum likelihood, asymptotic confidence intervals and applications using real data
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Bokde, Neeraj, Andrés Feijóo, and Daniel Villanueva. "Wind Turbine Power Curves Based on the Weibull Cumulative Distribution Function." Applied Sciences 8, no. 10 (September 28, 2018): 1757. http://dx.doi.org/10.3390/app8101757.

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The representation of a wind turbine power curve by means of the cumulative distribution function of a Weibull distribution is investigated in this paper, after having observed the similarity between such a function and real WT power curves. The behavior of wind speed is generally accepted to be described by means of Weibull distributions, and this fact allows researchers to know the frequency of the different wind speeds. However, the proposal of this work consists of using these functions in a different way. The goal is to use Weibull functions for representing wind speed against wind power, and due to this, it must be clear that the interpretation is quite different. This way, the resulting functions cannot be considered as Weibull distributions, but only as Weibull functions used for the modeling of WT power curves. A comparison with simulations carried out by assuming logistic functions as power curves is presented. The reason for using logistic functions for this validation is that they are very good approximations, while the reasons for proposing the use of Weibull functions are that they are continuous, simpler than logistic functions and offer similar results. Additionally, an explanation about a software package has been discussed, which makes it easy to obtain Weibull functions for fitting WT power curves.
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Pogány, Tibor k., and Ram k. Saxena. "The gamma-Weibull distribution revisited." Anais da Academia Brasileira de Ciências 82, no. 2 (June 2010): 513–20. http://dx.doi.org/10.1590/s0001-37652010000200026.

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The five parameter gamma-Weibull distribution has been introduced by Leipnik and Pearce (2004). Nadarajah and Kotz (2007) have simplified it into four parameter form, using hypergeometric functions in some special cases. We show that the probability distribution function, all moments of positive order and the characteristic function of gamma-Weibull distribution of a random variable can be explicitely expressed in terms of the incomplete confluent Fox-Wright Psi-function, which is recently introduced by Srivastava and Pogány (2007). In the same time, we generalize certain results by Nadarajah and Kotz that follow as special cases of our findings.
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ALWAKEEL, ALI HUSEEN. "ON DISCRETE WEIBULL DISTRIBUTION." Journal of Economics and Administrative Sciences 20, no. 79 (October 1, 2014): 1–9. http://dx.doi.org/10.33095/jeas.v20i79.1969.

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Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where 0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obtained as the discrete counterparts of either the distribution function or the failure rate function of the standard Weibull model. Which lead to different models. This paper discusses the discrete model which is the counterpart of the standard two-parameter Weibull distribution. It covers the determination of the probability mass function, cumulative distribution function, survivor function, hazard function, and the pseudo-hazard function.
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الوكيل, علي عبد الحسين. "ON DISCRETE WEIBULL DISTRIBUTION." Journal of Economics and Administrative Sciences 20, no. 79 (October 1, 2014): 1. http://dx.doi.org/10.33095/jeas.v20i79.807.

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Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assume the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables takes on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where 0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obtained as the discrete counter parts of either the distribution function or the failure rate function of the standard Weibull model. Which lead to different models. This paper discusses the discrete model which is the counter part of the standard two-parameter Weibull distribution. It covers the determination of the probability mass function, cumulative distribution function, survivor function, hazard function, and the pseudo-hazard function.
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Braimah, J. O., J. A. Adjekukor, N. Edike, and S. O. Elakhe. "A new Weibull Exponentiated Inverted Weibull Distribution for modelling positively-skewed data." Global Journal of Pure and Applied Sciences 27, no. 1 (March 5, 2021): 43–53. http://dx.doi.org/10.4314/gjpas.v27i1.6.

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An Exponentiated Inverted Weibull Distribution (EIWD) has a hazard rate (failure rate) function that is unimodal, thus making it less efficient for modeling data with an increasing failure rate (IFR). Hence, the need to generalize the EIWD in order to obtain a distribution that will be proficient in modeling these types of dataset (data with an increasing failure rate). This paper therefore, extends the EIWD in order to obtain Weibull Exponentiated Inverted Weibull (WEIW) distribution using the Weibull-Generator technique. Some of the properties investigated include the mean, variance, median, moments, quantile and moment generating functions. The explicit expressions were derived for the order statistics and hazard/failure rate function. The estimation of parameters was derived using the maximum likelihood method. The developed model was applied to a real-life dataset and compared with some existing competing lifetime distributions. The result revealed that the (WEIW) distribution provided a better fit to the real life dataset than the existing Weibull/Exponential family distributions.
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Ahmad, Zubair, and Zawar Hussain. "New Extended Weibull Distribution." Circulation in Computer Science 2, no. 6 (July 20, 2017): 14–19. http://dx.doi.org/10.22632/ccs-2017-252-31.

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This article considers a new function to propose a new lifetime model. The new model is introduced by utilizing the linear scheme of the two logarithms of cumulative hazard functions. The new model is named as new extended Weibull distribution, and is able to model data with unimodal or modified unimodal shaped failure rates. A brief explanation of the mathematical properties of the proposed model is provided. The model parameters will be estimated by deploying the maximum likelihood method. To illustrate the usefulness of the proposed model, an example will be discussed.
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Phani, K. K. "A New Modified Weibull Distribution Function." Journal of the American Ceramic Society 70, no. 8 (August 1987): C—182—C—184. http://dx.doi.org/10.1111/j.1151-2916.1987.tb05719.x.

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Hassan, Amal S., and Salwa M. Assar. "The Exponentiated Weibull-Power Function Distribution." Journal of Data Science 15, no. 4 (March 4, 2021): 589–614. http://dx.doi.org/10.6339/jds.201710_15(4).00002.

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Alizadeh, Morad, Muhammad Nauman Khan, Mahdi Rasekhi, and G.G Hamedani. "A New Generalized Modified Weibull Distribution." Statistics, Optimization & Information Computing 9, no. 1 (January 22, 2021): 17–34. http://dx.doi.org/10.19139/soic-2310-5070-1014.

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We introduce a new distribution, so called A new generalized modified Weibull (NGMW) distribution. Various structural properties of the distribution are obtained in terms of Meijer's $G$--function, such as moments, moment generating function, conditional moments, mean deviations, order statistics and maximum likelihood estimators. The distribution exhibits a wide range of shapes with varying skewness and assumes all possible forms of hazard rate function. The NGMW distribution along with other distributions are fitted to two sets of data, arising in hydrology and in reliability. It is shown that the proposed distribution has a superior performance among the compared distributions as evidenced via goodness--of--fit tests
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Dissertations / Theses on the topic "Weibull distribution function"

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Watkins, Adam Christopher. "RADIATION INDUCED TRANSIENT PULSE PROPAGATION USING THE WEIBULL DISTRIBUTION FUNCTION." OpenSIUC, 2012. https://opensiuc.lib.siu.edu/theses/811.

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In recent years, studying soft errors has become an issue of greater importance. There have been many methods developed that estimate the Soft Error Rate. Those methods are either deterministic or statistical. The proposed deterministic model aims to improve Soft Error Rate estimation by accurately approximating the generated pulse and all subsequent pulses. The generated pulse is approximated by a piecewise function consisting of two Weibull cumulative distribution functions. This method is an improvement over existing methods as it offers high accuracy while requiring less pre-characterization. The proposed algorithm reduces pre-characterization by allowing the beta Weibull parameter to be calculated during runtime using gate parameters such as the gate delay.
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Voytenko, Denis. "Modeling Direct Runoff Hydrographs with the Surge Function." Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/3398.

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A surge function is a mathematical function of the form f(x)=axpe-bx. We simplify the surge function by holding p constant at 1 and investigate the simplified form as a potential model to represent the full peak of a stream discharge hydrograph. The previously studied Weibull and gamma distributions are included for comparison. We develop an analysis algorithm which produces the best-fit parameters for every peak for each model function, and we process the data with a MATLAB script that uses spectral analysis to filter year-long, 15-minute, stream-discharge data sets. The filtering is necessary to locate the concave-upward inflection points used to separate the data set into its constituent, individual peaks. The Levenberg-Marquardt algorithm is used to iteratively estimate the unknown parameters for each version of the modeled peak by minimizing the sum of squares of residuals. The results allow goodness-of-fit comparisons between the three model functions, as well as a comparison of peaks at the same gage through the year of record. Application of these methods to five rivers from three distinct hydrologic regions shows that the simple surge function is a special case of the gamma distribution, which is known to be useful as a modeling function for a full-peak hydrograph. The study also confirms that the Weibull distribution produces good fits to 15-minute hydrograph data.
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Couto, Epaminondas de Vasconcellos. "Modelo de regressão log-gama generalizado exponenciado com dados censurados." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-16032010-112500/.

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No presente trabalho, e proposto um modelo de regressão utilizando a distribuição gama generalizada exponenciada (GGE) para dados censurados, esta nova distribuição e uma extensão da distribuição gama generalizada. A distribuição GGE (CORDEIRO et al., 2009) que tem quatro parâmetros pode modelar dados de sobrevivência quando a função de risco tem forma crescente, decrescente, forma de U e unimodal. Neste trabalho apresenta-se uma expansão natural da distribuição GGE para dados censurados, esta distribuição desperta o interesse pelo fato de representar uma família paramétrica que possui como casos particulares outras distribuições amplamente utilizadas na analise de dados de tempo de vida, como as distribuições gama generalizada (STACY, 1962), Weibull, Weibull exponenciada (MUDHOLKAR et al., 1995, 1996), exponencial exponenciada (GUPTA; KUNDU, 1999, 2001), Rayleigh generalizada (KUNDU; RAKAB, 2005), dentre outras, e mostra-se útil na discriminação entre alguns modelos probabilísticos alternativos. Considerando dados censurados, e abordado o método de máxima verossimilhança para estimar os parâmetros do modelo proposto. Outra proposta deste trabalho e introduzir um modelo de regressão log-gama generalizado exponenciado com efeito aleatório. Por fim, são apresentadas três aplicações para ilustrar a distribuição proposta.
In the present study, we propose a regression model using the exponentiated generalized gama (EGG) distribution for censored data, this new distribution is an extension of the generalized gama distribution. The EGG distribution (CORDEIRO et al., 2009) that has four parameters it can model survival data when the risk function is increasing, decreasing, form of U and unimodal-shaped. In this work comes to a natural expansion of the EGG distribution for censored data, is awake distribution the interest for the fact of representing a parametric family that has, as particular cases, other distributions which are broadly used in lifetime data analysis, as the generalized gama (STACY, 1962), Weibull, exponentiated Weibull (MUDHOLKAR et al., 1995, 1996), exponentiated exponential (GUPTA; KUNDU, 1999, 2001), generalized Rayleigh (KUNDU; RAKAB, 2005), among others, and it is shown useful in the discrimination among some models alternative probabilistics. Considering censored data, the maximum likelihood estimator is considered for the proposed model parameters. Another proposal of this work was to introduce a log-exponentiated generalized gamma regression model with random eect. Finally, three applications were presented to illustrate the proposed distribution.
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Yao, Fang. "Hazard functions and macroeconomic dynamics." Doctoral thesis, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, 2011. http://dx.doi.org/10.18452/16280.

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In dieser Arbeit werden die Folgen der Calvo-Annahme in dynamischen makroökonomischen Modellen untersucht. Dafür wird die Calvo-Annahme unter Anwendung des Konzepts der statistischen Hazardfunktion verallgemeinert. Ich untersuche zwei mögliche Anwendungen dieses Ansatzes innerhalb von DSGE-Modellen. Im ersten Artikel zeige ich, dass der Zugewinn an Handhabbarkeit, der aus der Calvo-Annahme für Neu-Keynesianische Modelle folgt, mit unerwünschten Folgen in Bezug auf die Inflationsdynamiken einher geht. Der zweite Artikel schätzt die aggregierte Hazardfunktion unter Verwendung des theoretischen Rahmens des ersten Artikels. Es zeigt sich, dass die Annahme einer konstanten Hazardfunktion, die aus der Calvo-Annahme folgt, von den Daten eindeutig abgelehnt wird. Im dritten Artikel analysiere ich die Implikationen der empirisch geschätzten Hazardfunktion für die Persistenz von Inflation und die Geldpolitik. Die Untersuchungen zeigen, dass mittels der empirisch plausiblen aggregierten Hazardfunktion Zeitreihen simuliert werden können, die mit der Persistenz der inflatorischen Lücke im US Verbraucherpreisindex konsistent sind. Anhand dieser Ergebnisse komme ich zu dem Schluss, dass die Hazardfunktion eine entscheidende Rolle für die dynamischen Eigenschaften von Inflation spielt. Der letzte Artikel wendet den selben Modellierungsansatz auf ein Real-Business-Cycle Model mit rigidem Arbeitsmarkt an. Unter Verwendung eines allgemeineren stochastischen Anpassungsprozess stelle ich fest, dass die Arbeitsmarktdynamiken von einem Parameter beinflusst werden, der das Monotonieverhalten der Hazardfunktion bestimmt. Insbesondere steigt die Volatilität des Beschäftigungsniveaus, wohingegen dessen Persistenz mit zunehmendem Parameterwert abnimmt.
The Calvo assumption (Calvo, 1983) is widely used in the macroeconomic literature to model market frictions that limit the ability of economic agents to re-optimize their control variables. In spite of its virtues, the Calvo assumption also implies singular adjustment behavior at the firm level as well as a restrictive aggregation mechanism for the whole economy. In this study, I examine implications of the Calvo assumption for macroeconomic dynamics. To do so, I extend the Calvo assumption to a more general case based on the concept of the statistical hazard function. Two applications of this approach are studied in the DSGE framework. In the first essay, I apply this approach to a New Keynesian model, and demonstrate that tractability gained from the Calvo pricing assumption is costly in terms of inflation dynamics. The second essay estimates aggregate price reset hazard function using the theoretical framework constructed in the first essay, and shows that the constant hazard function implied by the Calvo assumption is strongly rejected by the aggregate data. In the third essay, I further explore implications of the empirically based hazard function for inflation persistence and monetary policy. I find that the empirically plausible aggregate price reset hazard function can generate simulated data that are consistent with inflation gap persistence found in the US CPI data. Based on these results, I conclude that the price reset hazard function plays a crucial role for generating inflation dynamics. The last essay applies the same modeling approach to a RBC model with employment rigidity. I find that, when introducing a more general stochastic adjustment process, the employment dynamics vary with a parameter, which determines the monotonic property of the hazard function. In particular, the volatility of employment is increasing, but the persistence is decreasing in the value of the parameter.
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Scheffler, Christina, Theresa Förster, and Edith Mäder. "Beschleunigte Alterung von Glasfasern in alkalischen Lösungen: Einflüsse auf die mechanischen Eigenschaften." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1244042771688-80994.

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In alkalischen Lösungen führt die Reaktion von Hydroxylionen mit den Si-O-Si-Bindungen des Glasnetzwerks zur Bildung hydratisierter Oberflächen und gelöstem Silikat. Der Grad der Korrosion bzw. der Alterung der Glasfaser ist abhängig von der chemischen Zusammensetzung des Glases und Korrosionslösung sowie von Zeit und Temperatur. Die Untersuchung von Glasfasern verschiedener chemischer Zusammensetzung in NaOH- sowie Zementlösungen zeigte, dass die inhibierende Wirkung von Ca-Ionen zu einem veränderten Korrosionsmechanismus führt. Dies konnte anhand der mechanischen Eigenschaften der Glasfasern sowie rasterelektronenmikroskopischen Untersuchungen gezeigt werden. Während die Korrosion in NaOH-Lösung zu einer ausgeprägten Umwandlung der gesamten äußeren Glasfaserschicht in Reaktionsprodukte führte, zeigten Glasfasern in Zementlösung bei gleichem pH-Wert einen stark lokal begrenzten, punktförmigen Angriff. Daraus resultieren unterschiedliche mechanische Eigenschaften der Glasfasern in Abhängigkeit von der gewählten Korrosionslösung.
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Silva, Ana Rita Cordeiro da. "Uma abordagem probabilista da ruptura de painéis tracionados de concreto de granulometria fina armados com telas soldadas." Universidade de São Paulo, 2002. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-18072006-145508/.

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A resistência à ruptura de materiais frágeis como o concreto de granulometria fina é fortemente dependente de sua heterogeneidade, do tamanho da amostra e da heterogeneidade das tensões. A partir de uma abordagem probabilista, fundamentada no modelo de Weibull, este trabalho trata da influência de tais efeitos sobre a resistência à tração de painéis compósitos formados por concreto de granulometria fina e telas soldadas. Desde que as armaduras se mantenham em regime elástico, mostra-se que o modelo de Weibull de dois parâmetros pode ser empregado com sucesso na previsão da ruptura dos painéis compósitos em estudo. Os parâmetros foram então identificados com medidas de ensaios de flexão em três e em quatro pontos de barras de concreto de granulometria fina de dois tamanhos diferentes. A utilização do modelo de Weibull confirmou, por outro lado, a validade da teoria de misturas como ferramenta para estimar as resistências de rupturas locais correspondentes a diferentes níveis de formação de fissuras
The rupture strength of brittle materials such as the microconcrete is strongly dependent on the microstructural heterogeneity, the sample size and the stress heterogeneity. Using a probabilistic approach, based on the Weibull distribution, this work deals with the influence of such effects on the tensile strength of composite panels formed by microconcrete and welded wire grids. Provide the reinforcements behaves in elastic regime, it is shown that the model of Weibull of two parameters can be used with success to predict the failure of the composite panels studied. The parameters were then identified from measurements of flexural tests in three and in four points of two different sizes of microconcrete samples. The feasibility of the Weibull model validates, as well, the rule of mixture as a satisfactory tool to estimate local failure strengths of related to different levels of cracking
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Al-Malki, Saad Jamaan. "Statistical analysis of lifetime data using new modified Weibull distributions." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/statistical-analysis-of-lifetime-data-using-new-modified-weibull-distributions(0c8f3735-cc11-4189-b48e-99514c6110a2).html.

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The Weibull distribution is a popular and widely used distribution in reliability and in lifetime data analysis. Since 1958, the Weibull distribution has been modified by many researchers to allow for non-monotonic hazard functions. Many modifications of the Weibull distribution have achieved the above purpose. On the other hand, the number of parameters has increased, the forms of the survival and hazard functions have become more complicated and the estimation problems have risen. This thesis provides an extensive review of some discrete and continuous versions of the modifications of the Weibull distribution, which could serve as an important reference and encourage further modifications of the Weibull distribution. Four different modifications of the Weibull distribution are proposed to address some of the above problems using different techniques. First model, with five parameters, is constructed by considering a two-component serial system with one component following a Weibull distribution and another following a modified Weibull distribution. A new method has been proposed to reduce the number of parameters of the new modified Weibull distribution from five to three parameters to simplify the distribution and address the estimation problems. The reduced version has the same desirable properties of the original distribution in spite of having two less parameters. It can be an alternative distribution for all modifications of the Weibull distribution with bathtub shaped hazard rate functions. To deal with unimodal shaped hazard rates, the third model with four parameters, named as the exponentiated reduced modified Weibull distribution is introduced. This model is flexible, has a nice physical interpretation and has the ability to capture monotonically increasing, unimodal and bathtub shaped hazard rates. It is a generalization of the reduced modified Weibull distribution. The proposed distribution gives the best fit comparing to other modifications of the Weibull distribution including those having similar properties. A three-parameter discrete distribution is introduced based on the reduced distribution. It is one of only three discrete distributions allowing for bathtub shaped hazard rate functions. Four real data sets have applied to this distribution. The new distribution is shown to outperform at least three other models including the ones allowing for bathtub shaped hazard rate functions. The new models show flexibility and can be used to model different kinds of real data sets better than other modified versions of Weibull distribution including those having the same number of parameters. The mathematical properties and statistical inferences of the new models are studied. Based on a simulation study the performances of the MLEs of each model are assessed with respect to sample size n. We find no evidence that the generalized modified Weibull distribution can provide a better fit than the exponentiated Weibull distributionfor data sets exhibiting the modified unimodal hazard function.
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Mbah, Alfred Kubong. "On the theory of records and applications." [Tampa, Fla.] : University of South Florida, 2007. http://purl.fcla.edu/usf/dc/et/SFE0002216.

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Kuhlhoff, Igor Ribeiro. "Method for application of weibull distribution to the reliability calculation of functional safety for industrial machinery." reponame:Repositório Institucional da UFSC, 2014. https://repositorio.ufsc.br/xmlui/handle/123456789/132745.

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Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2014.
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O desenvolvimento de sistemas elétricos e eletrônicos permitiu a massificação do uso de dispositivos eletrônicos programáveis para comando e controle de operações de sistemas técnicos. Tais dispositivos possibilitaram o desenvolvimento de sistemas técnicos mais complexos, porém, devido a essa elevada complexidade, observou-se um aumento de acidentes causados por falhas inerentes ao controle de tais sistemas. Para se reduzir esses acidentes, foram criadas normas técnicas para sistemas de controle, cuja aplicação seja relevante a segurança, o que deu origem a segurança funcional. Segurança funcional refere-se à segurança que é mantida atráves do correto funcionamento de um sistema técnico. Diferentes segmentos industriais tem aplicado o conceito de segurança funcional, para criar máquinas e sistemas mais seguros. No setor de construção de máquinas, o uso de funções de segurança reduz o número de acidentes de trabalho, ao evitar que operadores, mantenedores e pessoas ao redor fiquem expostas aos perigos inerente das máquinas. As normas técnicos impõe requisitos quantitativos e qualitativos sobre os sistemas de controle de segurança. A norma técnica internacional IEC 61508 definiu um framework para quantificação de segurança funcional. Para cada setor industrial, normas específicas foram baseadas baseadas na IEC 61508. Esse framework é bem adequado para componentes elétricos e eletrônicos. Porém, na área de maquinário industrial, sistemas de controle são realizados não somente com tais componentes, mas também por componentes mecânicos, pneumáticos e hidráulicos, os quais apresentam um comportamento diferente de falha. Tais componentes são considerados pela norma técnica internacional ISO 13849. No entanto, os métodos de quantificação desta norma contém fortes limitações e não são completamente compreendidos pelos usuários. Este trabalho dedica-se ao estudo da norma técnica internacional de segurança funcional no setor de construção de máquinas industriais, a ISO 13849. O foco do estudo é a quantificação de falhas físicas de componentes. Falhas físicas sao quantificadas através de indicadores probabilísticos, sendo objeto de estudo da engenharia de confiabilidade. No primeiro capítulo, desenvolve-se o conceito de segurança funcional. O conceito é explorado como um todo, como uma ferramenta de redução de riscos, e posteriormente como esse conceito é aplicado no setor de construção de máquinas. O apêndice A complementa o capítulo 1 com a estrutura legal no que diz respeito à segurança de máquinas na Europa, definido pela Diretiva Europeia de Máquinas, da qual a norma técnica ISO 13849 faz parte. Ainda no capítulo 1 são identificadas as principais linhas de pesquisa, e o objetivo do trabalho é enunciado. Este trabalho, feito em parceria com a Bosch Rexroth, tem como objetivo o desenvolvimento de um método que possibilite a quatificação de índices de confiabilidade para segurança funcional utilizando distribuição de Weibull. No segundo capítulo, conceitos básicos para a compreensão do trabalho são apresentados. Os primeiros conceitos relacionam-se com conceitos da engenharia de confiabilidade, com o objetivo de esclarecer conceitos como probabilidade, confiabilidade, probabilidade de falha e construir o conceito do índice utilizado pela ISO 13849, a frequência média de falhas perigosas por hora, PFH. O apêndice B complementa esse capítulo, com uma explicação intuitiva do que é medido através do PFH. Neste capítulo também é apresentada a distribuição de Weibull, bem como métodos de cálculo de PFH. Os parâmetros para cálculo do PFH segundo a ISO 13849 são apresentados e explicados. No terceiro capítulo é apresentado como se é calculado o PFH através de simulação a eventos discretos. Um método para cálculo do PFH considerando distribuição de Weibull, para estruturas simples e estruturas redundantes, correspondendo às categorias B, 1, 3 e 4 da norma técnica ISO 13849. O apêndices C desenvolve a equação para determinaão do número mínimo de simulações para se alcançar o resultado desejado, e o apêndice D desenvolve as equações utilizadas pelo método proposto para estruturas redundantes com falha de componentes seguindo a distribuição de Weibull. Os resultados para os casos de comparação com a ISO 13849 são apresentados no apêndice E. No quarto capítulo é apresentado um exemplo de aplicação do método proposto em uma máquina hidráulica simples do Laboratório de Sistemas Hidráulicos e Pneumáticos (LASHIP), da Universidade Federal de Santa Catarina (UFSC). A determinação do PFH e subsequentemente do PL é realizada através do procedimento dado pela norma e pelo método proposto. Utilizando-se o método proposto, foi possível calcular PFH para intervalos de utilização diferente do considerado pela ISO 13849, bem como reconhecer o efeito do desgaste do componente, caracterizado pela distribuição de Weibull. No quinto capítulo é apresentado uma visão geral de como integrar o cálculo de PFH com distribuição de Weibull com o processo de desenvolvimento de uma máquina, baseado em experiência com a Bosch Rexroth. No capítulo de conclusão é analisado o potencial de se realizar análises mais realistas, e as limitações do método proposto, sendo adequado apenas para máquinas o subsistemas produzidos em série, devido ao requerimento de dados de campo para extrair os parâmetros da distribuição de Weibull para cada componente. Analisa-se também como que a pesquisa desenvolvida se encaixa na linha de pesquisa explicitada no primeiro capítulo, e qual a relevância para o cenário brasileiro. Adicionalmente, sugestões para trabalhos futuros são feitas.
Abstract : The IEC 61508 standard series defined a framework for quantification of functional safety. For each particular industry sector, specific standards are being developed based on it. This framework is well suited for electrical and electronic components. However, in the field of machinery, control systems are realized not only by such components, but also by mechanical, pneumatic and hydraulic components, which exhibit a different failure behavior. Such components are considered by the ISO 13849 standard. However, quantification methods of this standard are still not quite well understood by the users, and have strong limitations. This work presents a study an alternative method of how to calculate the average frequency of dangerous failures (PFH), required by ISO 13849 in order to achieve a Performance Level (PL). This alternative method includes modeling safety functions as Reliability Block Diagram and evaluation of PFH using the software BlockSim, through Discrete Event Simulation. Modeling hypothesis and limitations are discussed. The proposed method enables calculation of the standard s cases, as well as consideration of different failure distributions, of which Weibull distribution is considered. A study case considering Weibull distributed failures is presented. Applicability of the method is also discussed.
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Trönnberg, Filip. "Empirical evaluation of a Markovian model in a limit order market." Thesis, Uppsala universitet, Matematiska institutionen, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-176726.

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A stochastic model for the dynamics of a limit order book is evaluated and tested on empirical data. Arrival of limit, market and cancellation orders are described in terms of a Markovian queuing system with exponentially distributed occurrences. In this model, several key quantities can be analytically calculated, such as the distribution of times between price moves, price volatility and the probability of an upward price move, all conditional on the state of the order book. We show that the exponential distribution poorly fits the occurrences of order book events and further show that little resemblance exists between the analytical formulas in this model and the empirical data. The log-normal and Weibull distribution are suggested as replacements as they appear to fit the empirical data better.
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Books on the topic "Weibull distribution function"

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Gross, Bernard. Least squares best fit method for the three parameter Weibull distribution: Analysis of tensile and bend specimens with volume or surface flaw failure. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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United States. National Aeronautics and Space Administration., ed. Lower bound on reliability for Weibull distribution when shape parameter is not estimated accurately. [Washington, DC: National Aeronautics and Space Administration, 1990.

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Least squares best fit method for the three parameter Weibull distribution: Analysis of tensile and bend specimens with volume or surface flaw failure. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1996.

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J, Hu, Hopkins D. A, and Lewis Research Center, eds. An overview of engineering concepts and current design algorithms for probabilistic structural analysis. Cleveland, Ohio: NASA Lewis Research Center, 1995.

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Book chapters on the topic "Weibull distribution function"

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Singh, Nagendra Pratap, and Rajeev Srivastava. "Weibull Probability Distribution Function-Based Matched Filter Approach for Retinal Blood Vessels Segmentation." In Advances in Intelligent Systems and Computing, 427–37. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2525-9_40.

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Yang, yang, jianmin Zhang, Yi Wang, and Guiyan Hu. "Optimization and Simulation of Pre-warehouse Multi-objective Stock Levels Based on the Weibull Distribution Function." In Communications in Computer and Information Science, 484–95. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-8083-3_43.

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Quicke, Donald L. J., Buntika A. Butcher, and Rachel A. Kruft Welton. "Standard distributions in R." In Practical R for biologists: an introduction, 335–47. Wallingford: CABI, 2021. http://dx.doi.org/10.1079/9781789245349.0335.

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Abstract There are a number of in-built probability distributions, including uniform, binomial, negative binomial, normal, log-normal, logistic, exponential, Chisquared, Poisson, gamma, Fisher's F, Student's t, Weibull and others. These are used to generate p-values from test statistics, to generate random values from a distribution or to generate expected distributions. This chapter deals with standard distributions in R (a programming language that has a huge range of inbuilt statistical and graphical functions), focusing on the normal, Student's t, lognormal, logistic, Poisson, gamma, and the Chi-squared.
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Quicke, Donald L. J., Buntika A. Butcher, and Rachel A. Kruft Welton. "Standard distributions in R." In Practical R for biologists: an introduction, 335–47. Wallingford: CABI, 2021. http://dx.doi.org/10.1079/9781789245349.0030.

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Abstract There are a number of in-built probability distributions, including uniform, binomial, negative binomial, normal, log-normal, logistic, exponential, Chisquared, Poisson, gamma, Fisher's F, Student's t, Weibull and others. These are used to generate p-values from test statistics, to generate random values from a distribution or to generate expected distributions. This chapter deals with standard distributions in R (a programming language that has a huge range of inbuilt statistical and graphical functions), focusing on the normal, Student's t, lognormal, logistic, Poisson, gamma, and the Chi-squared.
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Kollia, Georgia D., Govind S. Mudholkar, and Deo Kumar Srivastava. "Estimation Using Quantile Function Structure with Emphasis on Weibull Distribution." In Advances in Multivariate Statistical Methods, 215–35. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812838247_0013.

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"Reliability Concepts." In EHT Transmission Performance Evaluation, 1–22. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-4941-3.ch001.

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The first chapter introduces basic concepts of Reliability and their relationships. Four probability functions—reliability function, cumulative distribution function, probability density function, and hazard rate function—that completely characterize the failure process are defined. Three failure rates—MTBF, MTTF, MTTR—that play important role in reliability engineering design process are explained here. The three patterns of failures, DFR, CFR, and IFR, are discussed with reference to the bathtub curve. Two probability models, Exponential and Weibull, are presented. Series and parallel systems and application areas of reliability are also presented.
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Kumar, Akshay, and Mangey Ram. "Reliability Analysis for Environment Systems Using Dual Hesitant Fuzzy Set." In Advanced Fuzzy Logic Approaches in Engineering Science, 162–73. IGI Global, 2019. http://dx.doi.org/10.4018/978-1-5225-5709-8.ch008.

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In this chapter, we deal with dual hesitant fuzzy set theory and compute the fuzzy reliability with lifetime components of different electronic systems, such as series and parallel systems from a Markov chain technique. In dual hesitant fuzzy sets, we have membership and non-membership degree function whereas hesitant fuzzy sets only have membership function. In this chapter we also discuss the Weibull distribution and reliability function of the proposed systems. A numerical example is also given in the end of proposed algorithm.
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Bhandari, Ashok Singh, Akshay Kumar, and Mangey Ram. "Fuzzy Reliability Evaluation of Complex Systems Using Intuitionistic Fuzzy Sets." In Advances in Systems Analysis, Software Engineering, and High Performance Computing, 166–80. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-7564-2.ch008.

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In a system where it cannot be reduced to a pure series and parallel form (i.e., complex), reliability is obtained by universal generating function (UGF) technique. The intuitionistic fuzzy sets (IFS) concept with triangular fuzzy number (TFN) and Weibull lifetime distribution is introduced to find the fuzzy reliability of the same system. Also, averaging operator with given equal weights is used with the set of three triangular intuitionistic fuzzy number. A numerical example is solved for demonstration.
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"Table of the gamma, digamma and trigamma functions." In The Weibull Distribution, 719–20. Chapman and Hall/CRC, 2008. http://dx.doi.org/10.1201/9781420087444-32.

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"Probability density and Weibull distribution functions." In Power Grids with Renewable Energy: Storage, integration and digitalization, 543–48. Institution of Engineering and Technology, 2020. http://dx.doi.org/10.1049/pbpo167e_appendixa.

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Conference papers on the topic "Weibull distribution function"

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Watkins, Adam, and Spyros Tragoudas. "Transient pulse propagation using the Weibull distribution function." In 2012 IEEE International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT). IEEE, 2012. http://dx.doi.org/10.1109/dft.2012.6378209.

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Hasegawa, Makoto, and Yuta Yanagitani. "Analysis of Contact Resistance Data with Weibull Distribution Function." In 2008 IEEE Holm Conference on Electrical Contacts (Holm 2008). IEEE, 2008. http://dx.doi.org/10.1109/holm.2008.ecp.66.

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Ali, Muhammad, Mazbah Kabir Mridul, and Abdullah Al Mahbub. "Comparative Wind Power Assessment by Weibull Distribution Function in Faridpur." In 2020 11th International Conference on Electrical and Computer Engineering (ICECE). IEEE, 2020. http://dx.doi.org/10.1109/icece51571.2020.9393088.

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Kar, R., A. Chattaraj, A. Chandra, A. K. Mal, and A. K. Bhattacharjee. "Delay Estimation for On-Chip VLSI Interconnect using Weibull Distribution Function." In 2008 IEEE Region 10 and the Third international Conference on Industrial and Information Systems (ICIIS). IEEE, 2008. http://dx.doi.org/10.1109/iciinfs.2008.4798399.

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Hou, Xiang, Rongxi He, Xudong Wang, Zheng Yang, and Rongxi He. "A new form of the moment generating function of Weibull distribution." In 2013 9th International Conference on Natural Computation (ICNC). IEEE, 2013. http://dx.doi.org/10.1109/icnc.2013.6818166.

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Wereszczak, Andrew A., Kristin Breder, Mark J. Andrews, Timothy P. Kirkland, and Mattison K. Ferber. "Strength Distribution Changes in a Silicon Nitride as a Function of Stressing Rate and Temperature." In ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/98-gt-527.

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Machining damage (a surface flaw) and porous-region-flaw (a volume flaw) populations limited the flexure strengths of a commercially available silicon nitride at 25°C, while these same flaws, along with inclusions, limited flexure strengths at 850°C. The machining damage and porous region flaws were the primary interest in the present study because they caused failure at both temperatures. Censoring revealed that the two-parameter Weibull strength distributions representing each flaw population changed as a function of stressing rate (i.e., dynamic fatigue) and temperature. A decrease in the Weibull scaling parameter is recognized as an indication of slow crack growth or time-dependent strength reduction in monolithic ceramics. Available life prediction codes used for reliability predictions of structural ceramic components consider the slow crack growth phenomenon. However, changes in the Weibull modulus are infrequently observed or reported, and typically are not accounted for in these life prediction codes. In the present study, changes in both Weibull parameters for the strength distributions provided motivation to the authors to survey what factors (e.g., residual stress, slow crack growth, and changes in failure mechanisms) could provide partial or full explanation of the observed distribution changes in this silicon nitride. Lastly, exercises were performed to examine the effects of strength distribution changes on the failure probability prediction of a diesel exhaust valve. Because the surface area and volume of this valve were substantially larger than those of the tested bend bars, it was found that the valve’s failure probability analysis amplified some slight or inconclusive distribution changes which were not evident from the interpretation of the censored bend bar strength data.
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Chen, Cheng-Yo, and Trevor Mills. "On Weibull Extreme Response of Offshore Structures." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-20476.

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This paper investigates the so-called two-parameter and three-parameter Weibull distribution functions with regard to their technical formulation and application to prediction of extreme responses of offshore structures. The validity of predicted Weibull extreme responses is evaluated using time-history responses of two floating structures (a Spar and a Truss Semi) and a fixed-base compliant tower platform. All these structures were previously designed for harsh environments in deepwater beyond 1,700 ft. in the Gulf of Mexico. The evaluation results indicate that the maximum responses predicted by both two-parameter and three-parameter Weibull distribution functions with a single 3-hr simulation agree well with those obtained from a more lengthy and rigorous process with numerous 3-hr time-history responses. It also shows that the predicted maxima from the two-parameter Weibull distribution function are more reliable and have less statistical variability than those from the three-parameter Weibull distribution function, particularly for highly nonlinear wide-banded non-Gaussian responses such as minimum air gaps at the cellar deck of the topsides of the floating structures. The approach using the two-parameter Weibull function as presented in this paper is thus an appealing tool in predicting maximum responses and will greatly improve the process in the early design stage of a fast track project.
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Kar, Rajib, Ashish K. Mal, and Anup K. Bhattacharjee. "An accurate slew metric for on-chip VLSI interconnect using Weibull distribution function." In the International Conference. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1523103.1523224.

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Bhonsle, Suryaji R., and Paul Thompson. "A Statistical Adaptable Distribution Function Model for Low Probabilities of Failure." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0063.

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Abstract Weibull, log normal, and some other Distribution function models (D.F.M.) have a tendency to deviate from experimental results. This deviation, either exceedingly conservative or nonconservative, is amplified at low probabilities of failure. To remedy such problems a new D.F.M. is derived. It is then used to predict low probabilities of failure. The predictions are consistent with experimental data and are not too conservative or too nonconservative.
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Bansal, Ajay, Anil Kumar, and Naresh Kumar. "Optimization of radial distribution system losses with wind weibull distribution function integration using PSO and GA technique." In 2016 7th India International Conference on Power Electronics (IICPE). IEEE, 2016. http://dx.doi.org/10.1109/iicpe.2016.8079378.

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