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The generalized inverse Weibull distribution

GUSMAO, Felipe R. S. de; ORTEGA, Edwin M. M.; CORDEIRO, Gauss M.
Fonte: SPRINGER Publicador: SPRINGER
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.63%
The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

The Kumaraswamy Weibull distribution with application to failure data

CORDEIRO, Gauss M.; ORTEGA, Edwin M. M.; NADARAJAH, Saralees
Fonte: PERGAMON-ELSEVIER SCIENCE LTD Publicador: PERGAMON-ELSEVIER SCIENCE LTD
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
56.55%
For the first time, we introduce and study some mathematical properties of the Kumaraswamy Weibull distribution that is a quite flexible model in analyzing positive data. It contains as special sub-models the exponentiated Weibull, exponentiated Rayleigh, exponentiated exponential, Weibull and also the new Kumaraswamy exponential distribution. We provide explicit expressions for the moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and Renyi entropy. The moments of the order statistics are calculated. We also discuss the estimation of the parameters by maximum likelihood. We obtain the expected information matrix. We provide applications involving two real data sets on failure times. Finally, some multivariate generalizations of the Kumaraswamy Weibull distribution are discussed. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

The beta modified Weibull distribution

SILVA, Giovana O.; ORTEGA, Edwin M. M.; CORDEIRO, Gauss M.
Fonte: SPRINGER Publicador: SPRINGER
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.72%
A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments and examine the order statistics and their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.; CAPES; CNPq

General results for the beta-modified Weibull distribution

NADARAJAH, Saralees; CORDEIRO, Gauss M.; ORTEGA, Edwin M. M.
Fonte: TAYLOR & FRANCIS LTD Publicador: TAYLOR & FRANCIS LTD
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.72%
We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the performances of the estimates from these methods. We obtain the expected information matrix. Two applications are presented to illustrate the proposed distribution.

A Log-Linear Regression Model for the Beta-Weibull Distribution

ORTEGA, Edwin M. M.; CORDEIRO, Gauss M.; HASHIMOTO, Elizabeth M.
Fonte: TAYLOR & FRANCIS INC Publicador: TAYLOR & FRANCIS INC
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.55%
We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.; CNPq; CAPES

INFERENCES FOR THE CHANGE-POINT OF THE EXPONENTIATED WEIBULL HAZARD FUNCTION

Mazucheli, Josmar; Coelho-Barros, Emilio Augusto; Achcar, Jorge Alberto
Fonte: INST NACIONAL ESTATISTICA-INE; LISBON Publicador: INST NACIONAL ESTATISTICA-INE; LISBON
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
56.45%
In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.

Modelo de regressão log-Weibull modificado e a nova distribuição Weibull modificada generalizada; Log-modified Weibull regression models and a new generalized modified Weibull distribution

Farfán Carrasco, Jalmar Manuel
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 09/11/2007 PT
Relevância na Pesquisa
66.72%
Neste trabalho propomos um modelo de regress~ao utilizando a distribuição Weibull modificado, esta distribuição pode ser usada para modelar dados de sobrevivência quando a de função de risco tem forma de U ou banheira. Assumindo dados censurados, é considerado os estimadores de máxima verossimilhança e Jackknife para os parâmetros do modelo proposto. Foram derivadas as matrizes apropriadas para avaliar influiência local sobre os parâmetros estimados considerando diferentes peturbações e também é apresen- tada alguma medidas de influência global. Para diferentes parâmetros fixados, tamanhos de amostra e porcentagem de censuras, varia simulações foram feitas para avaliar a distribuição empírica do resíduo deviance modificado e comparado coma distribuição normal padrão. Esses estudos sugerem que a distribuição empírica do resíduo devianve modificado para o modelo de regressão log-Weibull modificado com dados censurados aproxima-se de uma dis- tribuição normal padrão. Finalmente analisamos um conjunto de dados utilizando o modelo de regressão log-Weibull modificado. Uma nova distribuição de quatro parâmetros é definida para modelar dados de tempo de vida. Algumas propriedades da distribuição é discutida...

Modelos de regressão quando a função de taxa de falha não é monótona e o modelo probabilístico beta Weibull modificada; Regression models when the failure rate function is no monotone and the new beta modified Weibull model

Silva, Giovana Oliveira
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 05/02/2009 PT
Relevância na Pesquisa
46.74%
Em aplicações na área de análise de sobrevivência, é freqüente a ocorrência de função de taxa de falha em forma de U ou unimodal, isto e, funções não-monótonas. Os modelos de regressão comumente usados para dados de sobrevivência são log-Weibull, função de taxa de falha monótona, e log-logística, função de taxa de falha decrescente ou unimodal. Um dos objetivos deste trabalho e propor os modelos de regressão, em forma de locação e escala, log-Weibull estendida que apresenta função de taxa de falha em forma de U e log- Burr XII que tem como caso particular o modelo de regressão log-logística. Considerando dados censurados, foram utilizados três métodos para estimação dos parâmetros, a saber, máxima verossimilhança, bayesiana e jackkinife. Para esses modelos foram calculadas algumas medidas de diagnósticos de influência local e global. Adicionalmente, desenvolveu-se uma análise de resíduos baseada no resíduo tipo martingale. Para diferentes parâmetros taxados, tamanhos de amostra e porcentagens de censuras, várias simulações foram feitas para avaliar a distribuição empírica do resíduo tipo martingale e compará-la com a distribuição normal padrão. Esses estudos sugerem que a distribuição empírica do resíduo tipo martingale para o modelo de regressão log-Weibull estendida com dados censurados aproxima-se de uma distribuição normal padrão quando comparados com outros resíduos considerados neste estudo. Para o modelo de regressão log-Burr XII...

Estimação e diagnóstico na disribuição Weibull-Binomial-Negativa em análise de sobrevivência; Estimation and diagnosis for the Weibull-Negative-Binomial distribution in survival anaçysis

Yiqi, Bao
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 28/05/2012 PT
Relevância na Pesquisa
56.7%
Neste trabalho propomos a distribuição Weibull-Binomial-Negativa (WBN) considerando uma estrutura de ativação latente para explicar a ocorrência do evento de interesse, em que o número de causas competitivas é modelado pela distribuição Binomial Negativa, e os tempos não observados devido às causas seguem a distribuição Weibull. Em geral, as causas competitivas podem ter diferentes mecanismos de ativação, sendo assim os casos de primeira ativação, última ativação e ativação aleatória foram considerados no estudo. Desse modo o modelo proposto inclui uma ampla distribuição, tais como Weibull-Geométrico (WG) e Exponencial-Poisson Complementar (EPC), introduzidas por Barreto-Souza et al. (2011) e G. et al. (2011), respectivamente. Baseando-nos na mesma estrutura, consideramos o modelo de regressão locação-escala baseado na distribuição proposta (WBN) e o modelo para dados de sobrevivência com fração de cura. Os principais objetivos deste trabalho é estudar as propriedades matemáticas dos modelos propostos e desenvolver procedimentos de inferências desde uma perspectiva clássica e Bayesiana. Além disso, as medidas de diagnóstico Bayesiana baseadas na 'psi'-divergência (Peng & Dey, 1995; Weiss, 1996)...

Modelos multiníveis Weibull com efeitos aleatórios; Multilevel Weibull models with random effects

Hernandez Barajas, Freddy
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 28/02/2013 PT
Relevância na Pesquisa
56.63%
Os modelos multiníveis são uma classe de modelos úteis na análise de bases de dados com estrutura hierárquica. No presente trabalho propõem-se os modelos multiníveis com resposta Weibull, nos quais são considerados interceptos aleatórios na modelagem dos dois parâmetros da distribuição da variável resposta. Os modelos aqui propostos são flexíveis devido a que a distribuição dos interceptos aleatórios pode der escolhida entre uma das seguintes quatro distribuições: normal, log--gama, logística e Cauchy. Uma extensão dos modelos é apresentada na qual é possível incluir na parte sistemática dos dois parâmetros da distribuição da variável resposta interceptos e inclinações aleatórias com distribuição normal bivariada. A estimação dos parâmetros é realizada pelo método de máxima verossimilhança usando a quadratura de Gauss--Hermite para aproximar a função de verossimilhança. Um pacote em linguagem R foi desenvolvido especialmente para a estimação dos parâmetros, predição dos efeitos aleatórios e para a obtenção dos resíduos nos modelos propostos. Adicionalmente, por meio de um estudo de simulação foi avaliado o impacto nas estimativas dos parâmetros do modelo ao assumir incorretamente a distribuição dos interceptos aleatórios.; Multilevel models are a class of models useful in the analysis of datasets with hierarchical structure. In the present work we propose multilevel Weibull models in which random intercepts are considered to model the two parameters of the Weibull distribution. The proposed models are flexible due to random intercepts distribution can be chosen from one of the four following distributions: normal...

The gamma-Weibull distribution revisited

Pogány,Tibor k.; Saxena,Ram k.
Fonte: Academia Brasileira de Ciências Publicador: Academia Brasileira de Ciências
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2010 EN
Relevância na Pesquisa
66.51%
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.

Closed form expressions for moments of the beta Weibull distribution

Cordeiro,Gauss M; Simas,Alexandre B; Stošic,Borko D
Fonte: Academia Brasileira de Ciências Publicador: Academia Brasileira de Ciências
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2011 EN
Relevância na Pesquisa
66.52%
The beta Weibull distribution was first introduced by Famoye et al. (2005) and studied by these authors and Lee et al. (2007). However, they do not give explicit expressions for the moments. In this article, we derive explicit closed form expressions for the moments of this distribution, which generalize results available in the literature for some sub-models. We also obtain expansions for the cumulative distribution function and Rényi entropy. Further, we discuss maximum likelihood estimation and provide formulae for the elements of the expected information matrix. We also demonstrate the usefulness of this distribution on a real data set.

A new generalization of Weibull distribution with application to a breast cancer data set

Wahed, Abdus S.; Luong, The Minh; Jeong, Jong-Hyeon
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 20/07/2009 EN
Relevância na Pesquisa
46.65%
In this article, we propose a new generalization of the Weibull distribution, which incorporates the exponentiated Weibull distribution introduced by Mudholkar and Srivastava [1] as a special case. We refer to the new family of distributions as the beta-Weibull distribution. We investigate the potential usefulness of the beta-Weibull distribution for modeling censored survival data from biomedical studies. Several other generalizations of the standard two-parameter Weibull distribution are compared with regards to maximum likelihood inference of the cumulative incidence function, under the setting of competing risks. These Weibull-based parametric models are fit to a breast cancer dataset from the National Surgical Adjuvant Breast and Bowel Project (NSABP). In terms of statistical significance of the treatment effect and model adequacy, all generalized models lead to similar conclusions, suggesting that the beta-Weibull family is a reasonable candidate for modeling survival data.

Testes em modelos weibull na forma estendida de Marshall-Olkin

Magalhães, Felipe Henrique Alves
Fonte: Universidade Federal do Rio Grande do Norte; BR; UFRN; Programa de Pós-Graduação em Matemática Aplicada e Estatística; Probabilidade e Estatística; Modelagem Matemática Publicador: Universidade Federal do Rio Grande do Norte; BR; UFRN; Programa de Pós-Graduação em Matemática Aplicada e Estatística; Probabilidade e Estatística; Modelagem Matemática
Tipo: Dissertação Formato: application/pdf
POR
Relevância na Pesquisa
56.56%
In survival analysis, the response is usually the time until the occurrence of an event of interest, called failure time. The main characteristic of survival data is the presence of censoring which is a partial observation of response. Associated with this information, some models occupy an important position by properly fit several practical situations, among which we can mention the Weibull model. Marshall-Olkin extended form distributions other a basic generalization that enables greater exibility in adjusting lifetime data. This paper presents a simulation study that compares the gradient test and the likelihood ratio test using the Marshall-Olkin extended form Weibull distribution. As a result, there is only a small advantage for the likelihood ratio test; Universidade Federal do Rio Grande do Norte; Em análise de sobrevivência, a variável resposta e, geralmente, o tempo até a ocorrência de um evento de interesse, denominado tempo de falha, e a principal característica de dados de sobrevivência e a presença de censura, que é a observação parcial da resposta. Associados a essas informações, alguns modelos ocupam uma posição de destaque por sua comprovada adequação a várias situações práticas, entre os quais é possével citar o modelo Weibull. Distribuições na forma estendida de Marshall-Olkin oferecem uma generalização de distribuições básicas que permitem uma flexibilidade maior no ajuste de dados de tempo de vida. Este trabalho apresenta um estudo de simulação que compara duas estatísticas de teste...

An iterative method to obtain the specimen-independent three-parameter Weibull distribution of strength from bending tests

Przybilla, Constanze; Fernández Canteli, Alfonso; Castillo Ron, Enrique
Fonte: Elsevier Publicador: Elsevier
Tipo: info:eu-repo/semantics/article; publishedVersion
ENG
Relevância na Pesquisa
56.45%
Brittle materials, such as glass and ceramics, usually present a large strength scatter. Among other probability distributions, the Weibull distribution is widely used to characterize their resistance. Often the two-parameter model is employed, omitting the consideration of a threshold stress, leading to a simplified estimation method. For the sake of generality the present work uses fracture data from bending tests to obtain a three-parameter Weibull distribution function valid for a uni-axially and uniformly tensioned material element. The variable stress state prevailing in the flexural specimen and the size effect are simultaneously accounted for by means of an iterative fitting procedure. The method is extended to account for bimodal flaw distributions, discriminating between edge and surface failure results based on experimental observation. Finally, the model is applied to simulated data sets, obtaining satisfactory results.

Fracture strength: Stress concentration, extreme value statistics and the fate of the Weibull distribution

Bertalan, Zsolt; Shekhawat, Ashivni; Sethna, James P.; Zapperi, Stefano
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.67%
The fracture strength distribution of materials is often described in terms of the Weibull law which can be derived by using extreme value statistics if elastic interactions are ignored. Here, we consider explicitly the interplay between elasticity and disorder and test the asymptotic validity of the Weibull distribution through numerical simulations of the two-dimensional random fuse model. Even when the local fracture strength follows the Weibull distribution, the global failure distribution is dictated by stress enhancement at the tip of the cracks and sometimes deviates from the Weibull law. Only in the case of a pre-existing power law distribution of crack widths do we find that the failure strength is Weibull distributed. Contrary to conventional assumptions, even in this case, the Weibull exponent can not be simply inferred from the exponent of the initial crack width distribution. Our results thus raise some concerns on the applicability of the Weibull distribution in most practical cases.

The Weibull - Log Weibull Distribution for Interoccurrence Times of Earthquakes

Hasumi, Tomohiro; Akimoto, Takuma; Aizawa, Yoji
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.75%
By analyzing the Japan Meteorological Agency (JMA) seismic catalog for different tectonic settings, we have found that the probability distributions of time intervals between successive earthquakes --interoccurrence times-- can be described by the superposition of the Weibull distribution and the log-Weibull distribution. In particular, the distribution of large earthquakes obeys the Weibull distribution with the exponent $\alpha_1 <1$, indicating the fact that the sequence of large earthquakes is not a Poisson process. It is found that the ratio of the Weibull distribution to the probability distribution of the interoccurrence time gradually increases with increase in the threshold of magnitude. Our results infer that Weibull statistics and log-Weibull statistics coexist in the interoccurrence time statistics, and that the change of the distribution is considered as the change of the dominant distribution. In this case, the dominant distribution changes from the log-Weibull distribution to the Weibull distribution, allowing us to reinforce the view that the interoccurrence time exhibits the transition from the Weibull regime to the log-Weibull regime.; Comment: 11 pages, 5 figures

Inference on the parameters of the Weibull distribution using records

Jafari, Ali Akbar; Zakerzadeh, Hojatollah
Fonte: Universidade Autônoma de Barcelona Publicador: Universidade Autônoma de Barcelona
Tipo: Artigo de Revista Científica Formato: application/pdf
Publicado em //2015 ENG
Relevância na Pesquisa
66.48%
The Weibull distribution is a very applicable model for lifetime data. In this paper, we have investigated inference on the parameters of Weibull distribution based on record values. We first propose a simple and exact test and a confidence interval for the shape parameter. Then, in addition to a generalized confidence interval, a generalized test variable is derived for the scale parameter when the shape parameter is unknown. The paper presents a simple and exact joint confidence region as well. In all cases, simulation studies show that the proposed approaches are more satisfactory and reliable than previous methods. All proposed approaches are illustrated using a real example.

The exponentiated discrete Weibull distribution

Nekoukhou, Vahid; Bidram, Hamid
Fonte: Universidade Autônoma de Barcelona Publicador: Universidade Autônoma de Barcelona
Tipo: Artigo de Revista Científica Formato: application/pdf
Publicado em //2015 ENG
Relevância na Pesquisa
66.67%
In this paper, the exponentiated discrete Weibull distribution is introduced. This new generalization of the discrete Weibull distribution can also be considered as a discrete analogue of the exponentiated Weibull distribution. A special case of this exponentiated discrete Weibull distribution defines a new generalization of the discrete Rayleigh distribution for the first time in the literature. In addition, discrete generalized exponential and geometric distributions are some special sub-models of the new distribution. Here, some basic distributional properties, moments, and order statistics of this new discrete distribution are studied. We will see that the hazard rate function can be in- creasing, decreasing, bathtub, and upside-down bathtub shaped. Estimation of the parameters is illustrated using the maximum likelihood method. The model with a real data set is also examined

Mapping wind power density for Zimbabwe: a suitable Weibull-parameter calculation method

Hove,Tawanda; Madiye,Luxmore; Musademba,Downmore
Fonte: Journal of Energy in Southern Africa Publicador: Journal of Energy in Southern Africa
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/11/2014 EN
Relevância na Pesquisa
56.59%
The two-parameter Weibull probability distribution function is versatile for modelling wind speed frequency distribution and for estimating the energy delivery potential of wind energy systems if its shape and scale parameters, k and c, are correctly determined from wind records. In this study, different methods for determining Weibull k and c from wind speed measurements are reviewed and applied at four sample meteorological stations in Zimbabwe. The appropriateness of each method in modelling the wind data is appraised by its accuracy in predicting the power density using relative deviation and normalised root mean square error. From the methods considered, the graphical method proved to imitate the wind data most closely followed by the standard deviation method. The Rayleigh distribution (k=2 is also generated and compared with the wind speed data. The Weibull parameters were calculated by the graphical method for fourteen stations at which hourly wind speed data was available. These values were then used, with the assistance of appropriate boundary layer models, in the mapping of a wind power density map at 50m hub height for Zimbabwe. Keywords: Weibull distribution parameters, graphical method, power density.