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Generalized half-logistic Poisson distributions

  • Received : 2016.12.27
  • Accepted : 2017.06.03
  • Published : 2017.07.31

Abstract

In this article, we proposed a new three-parameter distribution called generalized half-logistic Poisson distribution with a failure rate function that can be increasing, decreasing or upside-down bathtub-shaped depending on its parameters. The new model extends the half-logistic Poisson distribution and has exponentiated half-logistic as its limiting distribution. A comprehensive mathematical and statistical treatment of the new distribution is provided. We provide an explicit expression for the $r^{th}$ moment, moment generating function, Shannon entropy and $R{\acute{e}}nyi$ entropy. The model parameter estimation was conducted via a maximum likelihood method; in addition, the existence and uniqueness of maximum likelihood estimations are analyzed under potential conditions. Finally, an application of the new distribution to a real dataset shows the flexibility and potentiality of the proposed distribution.

References

  1. Abdel-Hamid AH (2016). Properties, estimations and predictions for a Poisson-half-logistic distribution based on progressively type-II censored samples, Applied Mathematical Modelling, 40, 7164-7181. https://doi.org/10.1016/j.apm.2016.03.007
  2. Adamidis K, Dimitrakopoulou T, and Loukas S (2005). On an extension of the exponential-geometric distribution, Statistics & Probability Letters, 73, 259-269. https://doi.org/10.1016/j.spl.2005.03.013
  3. Adamidis K and Loukas S (1998). A lifetime distribution with decreasing failure rate, Statistics & Probability Letters, 39, 35-42. https://doi.org/10.1016/S0167-7152(98)00012-1
  4. Ali MM, Pal M, and Woo JS (2007). Some exponentiated distributions, Communications for Statistical Applications and Methods, 14, 93-109. https://doi.org/10.5351/CKSS.2007.14.1.093
  5. Arora SH, Bhimani GC, and Patel MN (2010). Some results on maximum likelihood estimators of parameters of generalized half logistic distribution under Type-I progressive censoring with changing failure rate, International Journal of Contemporary Mathematical Sciences, 5, 685-698.
  6. Barreto-SouzaWand Cribari-Neto F (2009). A generalization of the exponential-Poisson distribution, Statistics & Probability Letters, 79, 2493-2500. https://doi.org/10.1016/j.spl.2009.09.003
  7. Chung Y and Kang Y (2014). The exponentiated Weibull-geometric distribution: properties and estimations, Communications for Statistical Applications and Methods, 21, 147-160. https://doi.org/10.5351/CSAM.2014.21.2.147
  8. Cordeiro GM, Alizadeh M, and Ortega EM (2014). The exponentiated half-logistic family of distributions: properties and applications, Journal of Probability and Statistics, 2014, 1-21.
  9. Kang SB and Seo JI (2011). Estimation in an exponentiated half logistic distribution under progressively type-II censoring, Communications for Statistical Applications and Methods, 18, 657-666. https://doi.org/10.5351/CKSS.2011.18.5.657
  10. Kantam RRL, Ramakrishna V, and Ravikumar MS (2013). Estimation and testing in type I generalized half logistic distribution, Journal of Modern Applied Statistical Methods, 12, 198-206. https://doi.org/10.22237/jmasm/1367382060
  11. Krishnarani SD (2016). On a power transformation of half-logistic distribution, Journal of Probability and Statistics, 2016, 1-10.
  12. Kus C (2007). A new lifetime distribution, Computational Statistics & Data Analysis, 51, 4497-4509. https://doi.org/10.1016/j.csda.2006.07.017
  13. Lee ET and Wang JW (2003). Statistical Methods for Survival Data Analysis (3rd ed), Wiley, New York.
  14. Mahmoudi E and Jafari AA (2012). Generalized exponential-power series distributions, Computational Statistics & Data Analysis, 56, 4047-4066. https://doi.org/10.1016/j.csda.2012.04.009
  15. Mudholkar GS and Srivastava DK (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42, 299-302. https://doi.org/10.1109/24.229504
  16. Muhammad M (2016a). A generalization of the BurrXII-Poisson distribution and its applications, Journal of Statistics Applications & Probability, 5, 29-41. https://doi.org/10.18576/jsap/050103
  17. Muhammad M (2016b). Poisson-odd generalized exponential family of distributions: theory and Applications, Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics, https://doi.org/10.15672/hjms.2016.393. https://doi.org/10.15672/hjms.2016.393
  18. MuhammadM(2017). The complementary exponentiated BurrXII-Poisson distribution: model, properties and application, Journal of Statistics Applications & Probability, 6, 33-48. https://doi.org/10.18576/jsap/060104
  19. MuhammadMand Yahaya MA (2017). The half logistic-Poisson distribution, Asian Journal of Mathematics and Applications, 2017, 1-15.
  20. Nadarajah S and Haghighi F (2011). An extension of the exponential distribution, Statistics, 45, 543-558. https://doi.org/10.1080/02331881003678678
  21. Olapade AK (2014). The type I generalized half logistic distribution, Journal of Iranian Statistical Society, 13, 69-82.
  22. Pappas V, Adamidis K, and Loukas S (2015). A generalization of the exponential-logarithmic distribution, Journal of Statistical Theory and Practice, 9, 122-133. https://doi.org/10.1080/15598608.2014.898604
  23. Raja TA and Mir AH (2011). On extension of some exponentiated distributions with application, International Journal of Contemporary Mathematical Sciences, 6, 393-400.
  24. Seo JI, Kim Y, and Kang SB (2013). Estimation on the generalized half logistic distribution under Type-II hybrid censoring, Communications for Statistical Applications and Methods, 20, 63-75. https://doi.org/10.5351/CSAM.2013.20.1.063
  25. Seo JI, Lee HJ, and Kan SB (2012). Estimation for generalized half logistic distribution based on records, Journal of the Korean Data and Information Science Society, 23, 1249-1257. https://doi.org/10.7465/jkdi.2012.23.6.1249
  26. Silva RB, Barreto-SouzaW, and Cordeiro GM (2010). A new distribution with decreasing, increasing and upside-down bathtub failure rate, Computational Statistics & Data Analysis, 54, 935-944. https://doi.org/10.1016/j.csda.2009.10.006
  27. Silva RB and Cordeiro GM (2015). The Burr XII power series distributions: a new compounding family, Brazilian Journal of Probability and Statistics, 29, 565-589. https://doi.org/10.1214/13-BJPS234
  28. Tahmasbi R and Rezaei S (2008). A two-parameter lifetime distribution with decreasing failure rate, Computational Statistics & Data Analysis, 52, 3889-3901. https://doi.org/10.1016/j.csda.2007.12.002