Ir al contenido

Documat

A Reparameterized Weighted Lindley Distribution: Properties, Estimation and Applications

  • Autores: Alex L. Mota, Pedro L. Ramos, Paulo H. Ferreira, Vera Lucia D. Tomazella, Francisco Louzada Neto
  • Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 44, Nº. 1, 2021, págs. 65-90
  • Idioma: inglés
  • DOI: 10.15446/rce.v44n1.86566
  • Títulos paralelos:
    • Una distribución de Lindley ponderada reparametrizada: propiedades, estimación y aplicaciones
  • Enlaces
  • Resumen
    • español

      Resumen En este artículo, discutimos varias propiedades matemáticas y métodos de estimación para una versión reparametrizada de la distribución ponderada de Lindley (RWL). La distribución RWL puede ser particularmente útil para modelar datos de confiabilidad (supervivencia) con función de tasa de riesgo en forma de bañera o creciente. El procedimiento inferencial para obtener las estimaciones de los parámetros se realiza mediante el enfoque de máxima verosimilitud considerando la censura aleatoria a la derecha. Se realizan extensas simulaciones numéricas para investigar y evaluar el rendimiento del método de estimación propuesto. Finalmente, la utilidad del modelo RWL se analiza mediante el uso de dos conjuntos de datos reales.

    • English

      Abstract In this paper, we discuss several mathematical properties and estimation methods for a reparameterized version of the weighted Lindley (RWL) distribution. The RWL distribution can be particularly useful for modeling reliability (survival) data with bathtub-shaped or increasing hazard rate function. The inferential procedure to obtain the parameter estimates is conducted via the maximum likelihood approach considering random right-censoring. Extensive numerical simulations are carried out to investigate and evaluate the performance of the proposed estimation method. Finally, the potentiality of the RWL model is analyzed by employing two real data sets.

  • Referencias bibliográficas
    • Afify, A. Z.,Nassar, M.,Cordeiro, G. M.,Kumar, D. (2020). 'The Weibull Marshall-Olkin Lindley distribution: properties and estimation'....
    • Akaike, H. (1974). 'A new look at the statistical model identification'. IEEE Transactions on Automatic Control. 19. 716
    • Ali, S. (2015). 'On the bayesian estimation of the weighted Lindley distribution'. Journal of Statistical Computation and Simulation....
    • Asgharzadeh, A.,Bakouch, H. S.,Nadarajah, S.,Sharafi, F. (2016). 'A new weighted Lindley distribution with application. Brazilian Journal...
    • Asgharzadeh, A.,Nadarajah, S.,Sharafi, F. (2018). 'Weibull Lindley distribution'. REVSTAT Statistical Journal. 16. 87-113
    • Bakouch, H. S.,Al-Zahrani, B. M.,Al-Shomrani, A. A.,Marchi, V. A.,Louzada, F. (2012). 'An extended Lindley distribution'. Journal...
    • Bayoud, H. A. (2012). Bayesian Analysis of Type I Censored Data from Two-Parameter Exponential Distribution. 'Proceedings of the World...
    • Bourguignon, M.,Gallardo, D. I. (2020). 'Reparameterized inverse Gamma regression models with varying precision'. Statistica Neerlandica....
    • Bozdogan, H. (1987). 'Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions'....
    • Brent, R. P. (1973). Algorithms for Minimization without Derivatives. Prentice-Hall. Englewood Cliffs, New Jersey.
    • Bryson, M. C.,Siddiqui, M. (1969). 'Some criteria for aging'. Journal of the American Statistical Association. 64. 1472
    • Cepeda, E.,Gamerman, D. (2005). 'Bayesian methodology for modeling parameters in the two parameter exponential family'. Revista Estadística....
    • Cox, D. R.,Reid, N. (1987). 'Parameter orthogonality and approximate conditional inference'. ournal of the Royal Statistical Society:...
    • Cox, D. R.,Snell, E. J. (1968). 'A general definition of residuals'. Journal of the Royal Statistical Society: Series B (Methodological)....
    • Daniel, W. (1990). Applied Nonparametric Statistics. PWS-KENT Pub.
    • Ghitany, M.,Alqallaf, F.,Al-Mutairi, D. K.,Husain, H. (2011). 'A two-parameter weighted Lindley distribution and its applications to survival...
    • Ghitany, M. E.,Atieh, B.,Nadarajah, S. (2008). 'Lindley distribution and its application'. Mathematics and Computers in simulation....
    • Hannan, E. J.,Quinn, B. G. (1979). 'The determination of the order of an autoregression'. Journal of the Royal Statistical Society:...
    • Hasna, M. O.,Alouini, M.-S. (2004). 'Harmonic mean and end-to-end performance of transmission systems with relays'. IEEE Transactions...
    • Henningsen, A.,Toomet, O. (2011). 'maxLik: A package for maximum likelihood estimation in R'. Computational Statistics. 26. 443
    • Johnson, N. L.,Kotz, S.,Balakrishnan, N. (1994). Continuous univariate distributions. John Wiley & Sons.
    • Kemaloglu, S. A.,Yilmaz, M. (2017). 'Transmuted two-parameter Lindley distribution'. Communications in Statistics-Theory and Methods....
    • Khan, S. A. (2018). 'Exponentiated Weibull regression for time-to-event data'. Lifetime data analysis. 24. 328
    • Lawless, J. F. (2011). Statistical models and methods for lifetime data. John Wiley & Sons.
    • Limbrunner, J. F.,Vogel, R. M.,Brown, L. C. (2000). 'Estimation of harmonic mean of a lognormal variable'. Journal of hydrologic engineering....
    • Lindley, D. V. (1958). 'Fiducial distributions and Bayes' theorem'. Journal of the Royal Statistical Society. Series B (Methodological)....
    • Louzada, F.,Ramos, P. L. (2017). 'A new long-term survival distribution'. Biostatistics and Biometrics Open Access Journal. 1. 104
    • Louzada, F.,Ramos, P. L. (2018). 'Efficient closed-form maximum a posteriori estimators for the gamma distribution'. Journal ofStatistical...
    • Lukacs, E. (1972). 'A survey of the theory of characteristic functions'. Advances in Applied Probability. 4. 1-37
    • Manolakis, D. G.,Ingle, V. K.,Kogon, S. M. (2005). Statistical and adaptive signal processing. Artech House. Boston, London.
    • Mazucheli, J.,Coelho-Barros, E. A.,Achcar, J. A. (2016). 'An alternative reparametrization for the weighted Lindley distribution'....
    • Meeker, W. Q.,Escobar, L. A. (2014). Statistical methods for reliability data. John Wiley & Sons.
    • Olcay, A. H. (1995). 'Mean residual life function for certain types of non-monotonic ageing'. Communications in Statistics. Stochastic...
    • (2020). R Core Team R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria.
    • Raftery, A. E.,Newton, M. A.,Satagopan, J. M.,Krivitsky, P. N. (2006). Estimating the integrated likelihood via posterior simulation using...
    • Ramos, P. L.,Almeida, M. P.,Tomazella, V. L.,Louzada, F. (2019). 'Improved bayes estimators and prediction for the wilson-hilferty distribution'....
    • Ramos, P. L.,Louzada, F.,Cancho, V. G. (2017). 'Maximum likelihood estimation for the weighted Lindley distribution parameter under different...
    • Ramos, P.,Louzada, F. (2016). 'The generalized weighted Lindley distribution: Properties, estimation, and applications'. Cogent Mathematics....
    • Reed, W. J. (2011). 'A flexible parametric survival model which allows a bathtub-shaped hazard rate function'. Journal of Applied...
    • Rigby, R. A.,Stasinopoulos, M. D.,Heller, G. Z.,De Bastiani, F. (2019). Distributions for modeling location, scale, and shape: Using GAMLSS...
    • Santos-Neto, M.,Cysneiros, F. J. A.,Leiva, V.,Ahmed, S. E. (2012). 'On new parameterizations of the Birnbaum-Saunders distribution'....
    • Santos-Neto, M.,Cysneiros, F. J. A.,Leiva, V.,Barros, M. (2016). 'Reparameterized Birnbaum-Saunders regression models with varying precision'....
    • Schwarz, G. (1978). 'Estimating the dimension of a model'. The Annals of Statistics. 6. 461
    • Shanker, R.,Shukla, K. K.,Leonida, T. A. (2019). 'Weighted quasi Lindley distribution with properties and applications'. International...
    • Sugiura, N. (1978). 'Further analysts of the data by Akaike's information criterion and the finite corrections: Further analysts of...
    • Wienke, A. (2010). Frailty models in survival analysis. CRC press.
    • Yu, J. (2004). 'Empirical characteristic function estimation and its applications'. Econometric Reviews. 23. 93-123
    • Zakerzadeh, H.,Dolati, A. (2009). 'Generalized Lindley distribution'. Journal of Mathematical Extension. 3. 13-25
Los metadatos del artículo han sido obtenidos de SciELO Colombia
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno