The beta-burr type v distribution: its properties and application to real life data

  • Authors

    • Hussaini Garba Dikko Ahmadu Bello University, Zaria.
    • Yakubu Aliyu Ahmadu Bello University, Zaria.
    • Saidu Alfa Ahmadu Bello University, Zaria.
    2017-07-15
    https://doi.org/10.14419/ijasp.v5i2.7862
  • Burr Type V, Beta Burr V, Hazard Rate, Maximum Likelihood Estimation.

  • A new distribution called the beta-Burr type V distribution that extends the Burr type V distribution was defined, investigated and estab-lished. The properties examined provide a comprehensive mathematical treatment of the distribution. Additionally, various structural proper-ties of the new distribution verified include probability density function verification, asymptotic behavior, Hazard Rate Function and the cumulative distribution. Subsequently, we used the maximum likelihood estimation procedure to estimate the parameters of the new distribu-tion. Application of real data set indicates that this new distribution would serve as a good alternative distribution function to model real- life data in many areas.

  • References

    1. [1] Adepoju, K. A., and Chukwu, A. (2014). The Beta Power Exponential Distribution. Journal of Statistical Science and Application, 37-46.

      [2] Akaike, H. (1973). Information theory as an extension of the maximum likelihood principle. B. N. Petrov, and F. Csaki, (Eds.) Second International Symposium on Information Theory (pp. 267-281). Budapets: Akademia Kiado.

      [3] Akinsete, A., and Lowe, C. (2009). Beta-Rayleigh distribution in reliability measure. Proc Joint Stat Meet Phys Eng Science, 3103-3107.

      [4] AkinseteA, Famoye F, and Lee, C. (2008). The beta-pareto Distribution. Statistics, 547-563.https://doi.org/10.1080/02331880801983876.

      [5] Burr, W. I. (1942). Cumulative frequency distribution. Annals of Mathematical Statistics, 13, 215-232.https://doi.org/10.1214/aoms/1177731607.

      [6] Chukwu, A. U., and Ogunde, A. A. (2015). On the Beta Mekaham Distribution and Its Applications. 5, 137-143.

      [7] Dasgupta, R., and Sankhya, B. (2011). on the distribution of burr with applications. 73, 1- 19.https://doi.org/10.1007/s13571-011-0015-y.

      [8] Eugene, N., Lee, C., and Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics: Theory and Methods, 31, 497-512.https://doi.org/10.1081/STA-120003130.

      [9] Famoye, F., Lee, C., and Olugbenga, O. (2005). The beta-weibull distribution. Journal of Statistical Theory and Applications, 4 (2), 121-138.

      [10] Feroze, N. and Aslam, M. (2012). Bayesian analysis of Burr type X distribution under complete and censored samples, International Journal of Pure and Applied Sciences and Technology, 11, (2), 16-28.

      [11] Feroze, N. and Aslam, M. (2013). Maximum likelihood estimation of Burr type V distribution under left censored samples, wseas transactions on mathematics, 12, 657-669.

      [12] Fischer, M. and Vaughan, D. (2010). The beta-hyperbolic secant distribution. Austrian Journal of Statistics (39), 245-258.

      [13] Johnson, N. L., Kotz, S., and Balakrishnan, N. (1995). Continuous Univariate Distributions (2nd Edition ed., Vol. vol. 2). New York: Wiley.

      [14] Jones, M. C. (2004).Families of distributions arising from distributions of order statistics. Sociedad de EstadisticaeInvestigacionOperativa Test, 13 (1), 1-43.https://doi.org/10.1007/bf02602999.

      [15] Kong, L., Lee, C. and Sepanski, J. (2007). On the properties of beta-gamma distribution. Journal of Modern Applied Statistical Methods (6), 187-211.https://doi.org/10.22237/jmasm/1177993020.

      [16] Kozubowski, T., and Nadarajah, S, (2008). The beta-Laplace distribution. Journal of Computational Analysis and Applications, 10 (3), 305-318.

      [17] Merovci, F., Khaleel, M. A., Ibrahim, N. A., and Shitan, M. (2016). The beta Burr type X distribution properties with application. Springer, 1-18.https://doi.org/10.1186/s40064-016-2271-9.

      [18] Nadarajah, S. and Kotz, S. (2004). The beta-gumbel distribution. Mathematical Problems in Engineering, 1, 323-332.https://doi.org/10.1155/S1024123X04403068.

      [19] Nadarajah, S. and Kotz, S. (2006). The beta-exponential distribution. Reliability Engineering and System Safety, 91 (1), 689-697.https://doi.org/10.1016/j.ress.2005.05.008.

      [20] Nadarajah, S. and Gupta, A. (2004). The beta Fréchet distribution. Far East Journal of Theoritical Statistics 14, 15-24.

      [21] Paranaíba PF, Ortega EM, Cordeiro GM, Pescim RR (2011) the beta Burr XII distribution with application to lifetime data. Computational Statistics Data Analysis 55(2):1118–1136.https://doi.org/10.1016/j.csda.2010.09.009.

      [22] Shao, Q. (2004). Notes on maximum likelihood estimation for the three-parameter Burr XII distribution. Computational Statistics and Data Analysis, 45, 675-687.https://doi.org/10.1016/S0167-9473(02)00367-5.

      [23] Shittu, O. I., and Adepoju, K. A. (2013). On the Beta-Nakagami Distribution. Progress in Applied Mathematics, 5 (1), 49-58.

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