Zero-Truncated Poisson-Power Function Distribution

  • Idika Eke OkorieEmail author
  • Anthony Chukwudi Akpanta
  • Johnson Ohakwe
  • David Chidi Chikezie
  • Chris Uche Onyemachi
  • Manoj Kumar Rastogi


A three-parameter distribution with increasing, bathtub, and upside-down bathtub hazard rate characteristics is introduced. Various properties are discussed and nicely expressed in closed forms and the estimation of parameters is studied by the method of maximum likelihood. Numerical examples based on two real data-sets are presented.


Zero-truncated Poisson Power function Hazard rate Maximum likelihood 

Mathematics Subject Classification

62F10 62E15 60E05 



The authors would like to thank the referees and the Editor for their careful reading and comments which greatly improved the paper.


  1. 1.
    Adamidis K, Loukas S (1998) A lifetime distribution with decreasing failure rate. Stat Probab Lett 39(1):35–42CrossRefGoogle Scholar
  2. 2.
    Kuş C (2007) A new lifetime distribution. Comput Stat Data Anal 51(9):4497–4509CrossRefGoogle Scholar
  3. 3.
    Ristić MM, Nadarajah S (2014) A new lifetime distribution. J Stat Comput Simul 84(1):135–150CrossRefGoogle Scholar
  4. 4.
    Tahir MH, Zubair M, Cordeiro GM, Alzaatreh A, Mansoor M (2016) The Poisson-X family of distributions. J Stat Comput Simul 86(14):2901–2921CrossRefGoogle Scholar
  5. 5.
    Glaser RE (1980) Bathtub and related failure rate characterizations. J Am Stat Assoc 75(371):667–672CrossRefGoogle Scholar
  6. 6.
    Galton F (1883) Inquiries into human faculty and its development. Dent, London; (1928) Dutton, New YorkGoogle Scholar
  7. 7.
    Moors JJA (1988) A quantile alternative for Kurtosis. Statistician 37:25–32CrossRefGoogle Scholar
  8. 8.
    Hassan AS, Hemeda SE (2016) A new family of additive Weibull-generated distributions. Int J Math Appl 4(2–A):151–164Google Scholar
  9. 9.
    Barreto-Souza W, Cribari-Neto F (2009) A generalization of the exponential-Poisson distribution. Stat Probab Lett 79(24):2493–2500CrossRefGoogle Scholar
  10. 10.
    ul Haq MA, Butt NS, Usman RM, Fattah AA (2016) Transmuted power function distribution. Gazi Univ J Sci 29(1):177–185Google Scholar
  11. 11.
    Cramér H (1928) On the composition of elementary errors. Almqvist & Wiksells, StockholmGoogle Scholar
  12. 12.
    Von Mises R (1928) Statistik und Wahrheit. Springer, BerlinCrossRefGoogle Scholar
  13. 13.
    Anderson TW, Darling DA (1952) Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. Ann Math Stat 23:193–212CrossRefGoogle Scholar
  14. 14.
    Kolmogorov A (1933) Sulla determinazione empirica di una lgge di distribuzione. Inst Ital Attuari Giorn 4:83–91Google Scholar
  15. 15.
    Smirnoff N (1939) Sur les écarts de la courbe de distribution empirique. Mat Sb 48(1):3–26Google Scholar
  16. 16.
    Scheffé H (1943) Statistical inference in the non-parametric case. Ann Math Stat 14(4):305–332CrossRefGoogle Scholar
  17. 17.
    Wolfowitz J (1949) Non-parametric statistical inference. In: Proceedings of the Berkeley symposium on mathematical statistics and probability. University of California Press, Berkeley, CA, pp 93–113Google Scholar
  18. 18.
    Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19:716–723CrossRefGoogle Scholar
  19. 19.
    Schwarz GE (1978) Estimating the dimension of a model. Ann Stat 6:461–464CrossRefGoogle Scholar
  20. 20.
    Hurvich CM, Tsai C-L (1989) Regression and time series model selection in small samples. Biometrika 76:297–307CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsUniversity of ManchesterManchesterUK
  2. 2.Department of StatisticsAbia State UniversityUturuNigeria
  3. 3.Department of Mathematics and Statistics, Faculty of SciencesFederal University OtuokeYenagoaNigeria
  4. 4.National Institute of Pharmaceutical Education and ResearchHajipurIndia

Personalised recommendations