A generalisation of the exponential distribution and its applications on modelling skewed data

References

• Aarset, M. V. (1987). How to identify bathtub hazard rate. IEEE Transactions on Reliability, 36, 106–108. doi: 10.1109/TR.1987.5222310
   Web of Science ®Google Scholar
• Alzaatreh, A., Lee, C., & Famoye, F. (2013). A new method for generating families of continuous distributions. Metron, 71, 63–79. doi: 10.1007/s40300-013-0007-y
   Google Scholar
• Arnold, B. C., Balakrishnan, N., & Nagarajah, H. N. (2008). A first course in order statistics. New York: Wiley.
   Google Scholar
• Barlow, R. E., & Campo, R. A. (1975). Total time on test processes and applications to failure data analysis. In: R. E. Barlow, J. B. Fussel, & N. D. Singpurwalla (Eds.), Reliability and fault tree analysis (pp. 451–481). Philadelphia: Society for Industrial and Applied Mathematics.
   Google Scholar
• Bjerkedal, T. (1960). Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli. American Journal of Hygiene, 72, 130–148.
   PubMed Web of Science ®Google Scholar
• Dey, A. K., & Kundu, D. (2009). Discriminating among the log-normal, Weibull and generalized exponential distributions. IEEE Transactions on Reliability, 58, 416–424. doi: 10.1109/TR.2009.2019494
   Web of Science ®Google Scholar
• Gupta, R. C., Gupta, P. I., & Gupta, R. D. (1998). Modeling failure time data by Lehmann alternatives. Communications in Statistics – Theory and Methods, 27, 887–904. doi: 10.1080/03610929808832134
   Web of Science ®Google Scholar
• Gupta, R. D., & Kundu, D. (1999). Generalized exponential distribution. Australian & New Zealand Journal of Statistics, 41, 173–188. doi: 10.1111/1467-842X.00072
   Web of Science ®Google Scholar
• Gupta, R. D., & Kundu, D. (2001a). Generalized exponential distribution: An alternative to Gamma and Weibull distributions. Biometrical Journal, 43, 117–130. doi: 10.1002/1521-4036(200102)43:1<117::AID-BIMJ117>3.0.CO;2-R
   Web of Science ®Google Scholar
• Gupta, R. D., & Kundu, D. (2001b). Generalized exponential distribution: Different methods of estimations. Journal of Statistical Computation and Simulation, 69, 315–337. doi: 10.1080/00949650108812098
   Web of Science ®Google Scholar
• Gupta, R. D., & Kundu, D. (2002). Discriminating between the Weibull and the GE distributions. Computational Statistics and Data Analysis, 43, 179–196. doi: 10.1016/S0167-9473(02)00206-2
   Google Scholar
• Gupta, R. D., & Kundu, D. (2003). Closeness of gamma and generalized exponential distributions. Communications in Statistics– Theory and Methods, 32, 705–721. doi: 10.1081/STA-120018824
   Web of Science ®Google Scholar
• Gupta, R. D., & Kundu, D. (2004). Discriminating between the gamma and generalized exponential distributions. Journal of Statistical Computation and Simulation, 74, 107–121. doi: 10.1080/0094965031000114359
   Web of Science ®Google Scholar
• Gupta, R. D., & Kundu, D. (2006). On comparison of the Fisher information of the Weibull and GE distributions. Journal of Statistical Planning and Inference, 136, 3130–3144. doi: 10.1016/j.jspi.2004.11.013
   Web of Science ®Google Scholar
• Gupta, R. D., & Kundu, D. (2007). Generalized exponential distribution: Existing results and some recent developments. Journal of Statistical Planning and Inference, 137, 3537–3547. doi: 10.1016/j.jspi.2007.03.030
   Web of Science ®Google Scholar
• Gupta, R. D., & Kundu, D. (2008). Generalized exponential distribution: Bayesian Inference. Computational Statistics and Data Analysis, 52, 1873–1883. doi: 10.1016/j.csda.2007.06.004
   Google Scholar
• Gupta, R. D., & Kundu, D. (2011). An extension of generalized exponential distribution. Statistical Methodology, 8, 485–496. doi: 10.1016/j.stamet.2011.06.003
   Google Scholar
• Kenney, J., & Keeping, E. (1962). Mathematics of statistics (Vol. 1, 3rd ed.). Princeton, NJ: Van Nostrand.
   Google Scholar
• Kundu, D., Gupta, R. D., & Manglick, A. (2005). Discriminating between the log-normal and the generalized exponential distributions. Journal of Statistical Planning and Inference, 127, 213–227. doi: 10.1016/j.jspi.2003.08.017
   Web of Science ®Google Scholar
• Lehmann, E. L. (1953). The power of rank tests. Annals of Mathematical Statistics, 24, 23–43. doi: 10.1214/aoms/1177729080
   Google Scholar
• Moors, J. J. A. (1998). A quantile alternative for kurtosis. The Statistician, 37, 25–32. doi: 10.2307/2348376
   Google Scholar
• Nadarajah, S. (2011). The exponentiated exponential distribution: A survey. AStA Advances in Statistical Analysis, 95, 219–251. doi: 10.1007/s10182-011-0154-5
   Web of Science ®Google Scholar
• Nadarajah, S., & Kotz, S. (2006a). The exponentiated-type distributions. Acta Applicandae Mathematica, 92, 97–111. doi: 10.1007/s10440-006-9055-0
   Web of Science ®Google Scholar
• Nadarajah, S., & Kotz, S. (2006b). The beta exponential distribution. Reliability and Engineering System Safety, 91, 689–697. doi: 10.1016/j.ress.2005.05.008
   Web of Science ®Google Scholar
• Pakyari, R. (2010). Discriminating between generalized exponential, geometric extreme exponential and Weibull distribution. Journal of Statistical Computation and Simulation, 80, 1403–1412. doi: 10.1080/00949650903173306
   Web of Science ®Google Scholar
• Ristić, M. M., & Balakrishnan, N. (2012). The gamma-exponentiated exponential distribution. Journal of Statistical Computation and Simulation, 82, 1191–1206. doi: 10.1080/00949655.2011.574633
   Web of Science ®Google Scholar
• Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379–432. doi: 10.1002/j.1538-7305.1948.tb01338.x
   Web of Science ®Google Scholar
• Smith, R. L., & Naylor, J. C. (1987). A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Applied Statistics, 36, 358–369. doi: 10.2307/2347795
   Web of Science ®Google Scholar
• von Mises, R. (1936). La distribution de la plus grande de n valeurs. Revue Mathematique de lUnion Interbalcanique, 1, 141–160.
   Google Scholar