A New Log-location Regression Model with Influence Diagnostics and Residual Analysis

Emrah Altun, Haitham M. Yousof, GG Hamedani

DOI Number
https://doi.org/10.22190/FUMI1803417A
First page
417
Last page
449

Abstract


A new four-parameter lifetime model called OddLog-Logistic Burr XII distribution, is defined and investigated. Some of itsmathematical properties are derived. Some useful characterization resultsbased on \ the ratio of two truncated moments, based on the hazard functionas well as on the conditional expectation of certain functions of the randomvariable are presented. The maximum likelihood method is used to estimatethe model parameters by means of a graphical Monte Carlo simulation study.Moreover, we introduce a new log-location regression model based on theproposed distribution. The Jackknife estimation method as an alternativemethod is used to estimate the unknown parameters of new regression model. Thegeneralized cook distance and likelihood distance measures are used todetect the possible influential observations. The martingale and modifieddeviance residuals are defined to detect outliers and evaluate the modelassumptions. The potentiality of the new regression model is illustrated bymeans of a real data set.

Keywords

Regression Model; Burr XII Distribution; Residual Analysis; Influential Diagnostics; Simulation; Jackknife Estimation Method

Keywords


Regression Model; Burr XII Distribution; Residual Analysis; Influential Diagnostics; Simulation; Jackknife Estimation Method

Full Text:

PDF

References


bibitem{} Afify, A. Z., Cordeiro, G.M., Ortega, E. M. M. Yousof, H. M. and

Butt, N. S. (2015). The four-parameter Burr XII distribution: properties,

regression model and applications. Communications in StatisticsTheory and Method, forthcoming.

bibitem{} Abramowitz, M., Stegun, I.A., 1964. Handbook of Mathematical

Functions, Washington.

bibitem{} Burr, I. W. (1942). Cumulative frequency functions. Annals of

Mathematical Statistics, 13, 215-232.

bibitem{} Burr, I. W. (1968). On a general system of distributions, III.The

simplerange.Journal of the American Statistical Association, 63, 636-643.

bibitem{} Burr, I. W. (1973). Parameters fora general system of

distributions to match a grid of 3 and 4.Communications in Statistics, 2,

-21.

bibitem{} Burr, I. W. and Cislak, P. J. (1968). On a general system of

distributions: I. Its curveshaped characteristics; II. The sample median.

Journalof the American Statistical Association, 63, 627-635

bibitem{} Cordeiro, G. M., Yousof, H. M., Ramires, T. G. and Ortega, E. M. M. (2017). The Burr XII system of densities: properties, regression model and applications. Journal of Statistical Computation and Simulation, forthcoming.

bibitem{} Glanzel, W., (1987). A characterization theorem based on

truncated moments and its application to some distribution families,

Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986),

Vol. B, Reidel, Dordrecht, 75--84.

bibitem{} Glanzel, W., (1990). Some consequences of a characterization

theorem based on truncated moments, Statistics: A Journal of Theoretical and

Applied Statistics, 21 (4), 613--618.

bibitem{} Gleaton, J.U. and Lynch, J.D. (2006). Properties of generalized

log-logistic families of lifetime distributions. Journal of Probability and

Statistical Science, 4, 51-64.

bibitem{} Gradshteyn, I.S., Ryzhik, I.M., 2000. Table of Integrals, Series and Products, sixth ed.. Academic Press, San Diego.

bibitem{} Hamedani, G.G., (2013). On certain generalized gamma

convolution distributions $II$, Technical Report, No. 484, MSCS, Marquette

University.

bibitem{} Hatke, M. A. (1949). A certain cumulative probability function.

Annals of Mathematical Statistics, 20, 461-463

bibitem{} Hosmer, D. W. and Lemeshow, S. (1998). Applied Survival Analysis: Regression Modeling of Time to Event Data. John Wiley $&$ Sons.

bibitem{} Parana'{i}ba, P. F., Ortega, E. M. M., Cordeiro, G. M. and Pescim,

R. R. (2011). The beta Burr XII distribution with application to lifetime

data. Computation Statistics and Data Analysis, 55, 1118-1136.

bibitem{} Prudnikov, A. P., Brychkov, Y. A. and Marichev, O. I. (1986).

Integrals and Series, 1. Gordon and Breach Science Publishers, Amsterdam.

bibitem{} Prudnikov, A. P., Brychkov, Y. A. and Marichev, O. I. (1992).

Integrals and Series, 4. Gordon and Breach Science Publishers, Amsterdam.

bibitem{} Rodriguez, R.N. (1977). A guide to the Burr type XII

distributions. Biometrika, 64, 129-134.

bibitem{} Silva, G. O., Ortega, E. M. M., Garibay, V. C. and Barreto, M. L.

(2008). Log-Burr XII regression models with censored data. Computational

Statistics and Data Analysis, 52, 3820-3842.

bibitem{} Silva, G. O., Ortega, E. M. M., Paula, G.A. (2010b). Residuals

for logBurr XII regression models in survival analysis. Journal of Applied

Statistics. doi:10.1080/02664763.2010.505950

bibitem{} Soliman, A.A. (2005). Estimation of parameters of life from

progressively censored data

bibitem{} using Burr-XII Model. IEEE Transactions on Reliability, 54,

{42.

bibitem{} Tadikamalla, P. R. (1980). A look at the Burr and related

distributions, International Statistical Review, 48, 337-344.

bibitem{} Shao, Q. (2004). Notes on maximum likelihood estimation for the

three-parameter Burr XII distribution . Computational Statistics and Data

Analysis, 45, 675-687.

bibitem{} Yousof, H. M., Altun, E., Rasekhi, M., Alizadeh, M. Hamedani G.

G. and Ali M. M. (2017). A new lifetime model with regression model,

characterizations and applications. Communications in Statistics -

Simulation and Computation, forthcoming.

bibitem{} Zimmer, W. J., Keats, J. B. and Wang, F. K. (1998). The Burr XII

distribution in reliability analysis. Journal of Quality Technology, 30,

-394.

bibitem{} Xu, K., Xie, M., Tang, L. C., & Ho, S. L. (2003). Application of neural networks in forecasting engine systems reliability. Applied Soft Computing, 2(4), 255-268.




DOI: https://doi.org/10.22190/FUMI1803417A

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)