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Abstract

In this paper, a new generalization of Log Logistic Distribution using Alpha Power Transformation is proposed. The new distribution is named Alpha Power Log-Logistic Distribution. A comprehensive account of some of its statistical properties are derived. The maximum likelihood estimation procedure is used to estimate the parameters. The importance and utility of the proposed model are proved empirically using two real life data sets.

Keywords

Alpha Power Log Logistic Distribution Reliability analysis Entropy Maximum Likelihood Estimation

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How to Cite
Malik, A. S., & Ahmad, S. (2020). An Extension of Log-Logistic Distribution for Analyzing Survival Data. Pakistan Journal of Statistics and Operation Research, 16(4), 789-801. https://doi.org/10.18187/pjsor.v16i4.2961

References

  1. Aryal, G. (2013). Transmuted Log-Logistic distribution. Journal of Statistics Applications & Probability, 2(1):11–20.
  2. Ashkar, F. and Mahdi, S. (2006). Fitting the Log-Logistic distribution by generalized moments. Journal of Hydrology, 328:694–703.
  3. Bacon, R. W. (1993). A note on the use of the log-logistic functional form for modeling saturation effects. Oxford Bulletin of Economics and Statistics, 55:355–361.
  4. Collet, D. (2003). Modelling Survival data in medical research. Chapman and Hall, London.
  5. Diekmann, A. (1992). The Log-Logistic distribution as a model for social diffusion processes. Journal Scientific and Industrial Research, 51:285–290.
  6. Gui, W. (2013). Marshall-Olkin Extended Log-Logistic distribution and its Application in Minification Pro- cesses. Applied Mathematical Sciences, 7(80):3947–3961.
  7. Kleiber, C. and Kotz, S. (2003). Statistical Size distributions in Economics and Actuarial Sciences. Wiley, New York.
  8. Lemonte, A. J. (2014). The beta Log-Logistic distribution. Brazilian Journal of Probability and Statistics, 8(3):313–332.
  9. Little, C. L., Adams, M. R., Anderson, W. A., and Cole, M. B. (1994). Application of a log-logistic model to describe the survival of Yersinia enterocolitica at sub-optima ph and temperature. International Journal of Food Microbiology, 22(1):63–71.
  10. Mahadavi, A. and Kundu, D. (2015). A new method of generating distribution with an application to expo- nential distribution. Communications in Statistics - Theory and Applications, 46(13):6543–6557.
  11. Murthy, D., Xie, M., and Jiang, R. (2004). Weibull Models, Wiley Series in Probability and Statistics. John Wiley and Sons, New York.
  12. Nandram, B. (1989). Discrimination between the complimentary log-log and logistic model for ordinal data. Communications in Statistics - Theory and Applications, 1(8):21–55.
  13. Renyi, A. (1961). On Measures of Information and Entropy. Proceedings of the Fourth Berkeley Symposium On Mathematics, Statistics And Probability, NA:547–561.
  14. Santana, T. V. F., Ortega, E. M. M., Cordeiro, G. M., and Silva, G. O. (2012). The Kumaraswamy-Log- Logistic distribution. Journal of Statistical Theory and Applications, 11(3):265–291.
  15. Singh, K. P., Lee, C. M. S., and George, E. O. (1988). On generalized log logistic model for censored survival data. Biometrical Journal, 30(7):843–850.