A New Distribution for Modeling Lifetime Data with Different Methods of Estimation and Censored Regression Modeling

  • Mohamed Ibrahim Damietta University
  • Emrah Altun EA Bartin University
  • Haitham M. Yousof Benha University
DOI: https://doi.org/10.19139/soic-2310-5070-678
Keywords: Burr XII Distribution, Censored Data, Residual Analysis, Bootstraping, Least Square, Weighted Least Square.

Abstract

In this paper and after introducing a new model along with its properties, we estimate the unknown parameter of the new model using the Maximum likelihood method, Cram er-Von-Mises method, bootstrapping method, least square method and weighted least square method. We assess the performance of all estimation method employing simulations. All methods perform well but bootstrapping method is the best in modeling relief times whereas the maximum likelihood method is the best in modeling survival times. Censored data modeling with covariates is addressed along with the index plot of the modified deviance residuals and its Q-Q plot.

References

M. Alizadeh, M. Emadi and M. Doostparast A New Two-Parameter Lifetime Distribution: Properties, Applications and Different Method of Estimations, Statistics, Optimization & Information Computing, vol. 7, 291-310, 2019.

E. Altun, H. M. Yousof and G. G. Hamedani A new generalization of generalized half-normal distribution: properties and regression models, Journal of Statistical Distributions and Applications, vol. 5, 1-16., 2018.

T. Bjerkedal Acquisition of resistance in Guinea pigs infected with different doses of virulent tubercle bacilli, American Journal of Hygiene, vol. 72, 130–148, 1960

G. M. Cordeiro, H. M. Yousof, T. G. Ramires and E. M. Ortega The Burr XII system of densities: properties, regression model and applications, Journal of Statistical Computation and Simulation, vol. 88, 432-456, 2018.

R. C. Gupta, P. L. Gupta and R. D. Gupta Modeling failure time data by Lehmann alternatives, Communications in Statistics Theory Methods, vol. 27, 887-904, 1998.

R. D. Gupta and D. Kundu Exponentiated exponential family: an alternative to gamma and Weibull distributions, Biometrical Journal: Journal of Mathematical Methods in Biosciences, vol. 43, 117–130, 2001.

R. D. Gupta and D. Kundu Generalized exponential distribution: existing results and some recent developments, Journal of Statistical Planning and Inference, vol. 137, 3537–3547, 2007.

J. Gross and V. A. Clark Survival Distributions: Reliability Applications in the Biometrical Sciences, John Wiley, New York, USA, 1975.

M. C. Korkmaz, E. Altun, M. Alizadeh and H. M. Yousof A new flexible lifetime model with log-location regression modeling, properties and applications, Journal of Statistics and Management Systems, 1-21, 2019.

P. D. M. MacDonald Comment on An estimation procedure for mixtures of distributions by Choi and Bulgren, Journal of the Royal Statistical Society. Series B, vol. 33, 326-329, 1971.

C. A. McGilchrist and C. W. Aisbett Regression with frailty in survival analysis, Biometrics, vol. 47, 461-466, 1991.

M. Mozafari, M. Afshari, M. Alizadeh, H. Karamikabir The Zografos-Balakrishnan Odd Log-Logistic Generalized Half-Normal Distribution with Mathematical Properties and Simulations, Statistics, Optimization & Information Computing, vol. 7, 211-234, 2019.

S. Nadarajah The exponentiated exponential distribution: a survey, AStA Advances in Statistical Analysis, vol. 95, 219–251, 2011.

J. J. Swain, S. Venkatraman and J. R. Wilson Least-squares estimation of distribution functions in Johnson’s translation system, Journal of Statistical Computation and Simulation, 29(4), 271-297, 1988.

H. M. Yousof, E. Altun, M. Rasekhi, M. Alizadeh, G. G. Hamedani and M. M. Ali A new lifetime model with regression models, characterizations and applications, Communications in Statistics-Simulation and Computation, vol. 48, 264-286,2019

Published
2020-05-28
How to Cite
Ibrahim, M., EA, E. A., & Yousof, H. M. (2020). A New Distribution for Modeling Lifetime Data with Different Methods of Estimation and Censored Regression Modeling. Statistics, Optimization & Information Computing, 8(2), 610-630. https://doi.org/10.19139/soic-2310-5070-678
Issue
Vol 8 No 2 (2020)
Section
Research Articles
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