A Three Parameter Power Nakagami Distribution: Properties and Application on the Tax Revenue Data

Main Article Content

Shakila Bashir, Noor Waseem, Mujahid Rasul


Developing the probability distributions is increasing extensively over the decades but even though the newly developed distributions have elegant properties and variety of shapes which are applicable in wide areas of real-life situations and a numerous type of data sets. In this article, we introduced a three-parameter positively skewed model named Power Nakagami (PN) distribution based on power transformation. Various statistical properties of the Power Nakagami distribution are derived, including moments. Some reliability measures such as survival function, hazard function, cumulative hazard function and reversed hazard function are discussed also expressions for mills ratio, odd function, elasticity and Lorenz and Bonferroni Curve are developed. Graphical representation of probability density function, cumulative density function and reliability measures are presented. Maximum likelihood estimation is used to estimate the parameters. The distribution is fitted to real life dataset (Tax revenue) to demonstrate the comparison of the new distribution with the base distribution.

Article Details


  1. S.M. Ahad, S.P. Ahmad, Characterization and Estimation of the Length Biased Nakagami Distribution, Pak. J. Stat. Oper. Res. 14 (2018), 697-715. https://doi.org/10.18187/pjsor.v14i3.1930.
  2. I. Ahmad, Shafiq-ul-Rehman, Parameters Estimation of Nakagami Probability Distribution Using Methods of L.Moments, NUST J. Eng. Sci. 8 (2015), 10-13.
  3. K.A. Adepoju, A.U. Chukwu, O.I. Shittu, Statistical Properties of The Exponentiated Nakagami Distribution, J. Math. Syst. Sci. 4 (2014), 180-185.
  4. M.E. Ghitany, D.K. Al-Mutairi, N. Balakrishnan, L.J. Al-Enezi, Power Lindley Distribution and Associated Inference, Comput. Stat. Data Anal. 64 (2013), 20-33. https://doi.org/10.1016/j.csda.2013.02.026.
  5. S.D. Krishnarani, On a Power Transformation of Half-Logistic Distribution, J. Prob. Stat. 2016 (2016), 2084236. https://doi.org/10.1155/2016/2084236.
  6. M. Nakagami, The m-Distribution-A General Formula of Intensity Distribution of Rapid Fading, in: Statistical Methods in Radio Wave Propagation, Elsevier, 1960: pp. 3-36. https://doi.org/10.1016/B978-0-08-009306-2.50005-4.
  7. M. Nassar, N.K. Nada, The Beta Generalized Pareto Distribution, J. Stat.: Adv. Theory Appl. 6 (2011), 1-17.
  8. H. Okagbue, M.O. Adamu, T.A. Anake, Closed Form Expression for the Inverse Cumulative Distribution Function of Nakagami Distribution, Wireless Netw. 26 (2020), 5063-5084. https://doi.org/10.1007/s11276-020-02384-2.
  9. E.H.A. Rady, W.A. Hassanein, T.A. Elhaddad, The Power Lomax Distribution With an Application to Bladder Cancer Data, SpringerPlus. 5 (2016), 1838. https://doi.org/10.1186/s40064-016-3464-y.
  10. S. Sharma, K.K. Das, Weighted Inverse Nakagami Distribution, Thailand Statistician, 19 (2021), 698-720.
  11. M. Shrahili, N. Alotaibi, D. Kumar, A.R. Shafay, Inference on Exponentiated Power Lindley Distribution Based on Order Statistics with Application, Complexity. 2020 (2020), 4918342. https://doi.org/10.1155/2020/4918342.
  12. L. Wang, S. Dey, Y.M. Tripathi, Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples, Mathematics. 10 (2022), 2137. https://doi.org/10.3390/math10122137.