The Transmuted Inverse Exponential Distribution

  • Authors

    • Pelumi Oguntunde Covenant University
    • Olusola Adejumo University of Ilorin, Kwara State, Nigeria
    2014-12-12
    https://doi.org/10.14419/ijasp.v3i1.3684
  • Generalization, Inverse Exponential, Moments, Quadratic Rank Transmuted Map, Quantile Function, Transmuted Inverse Exponential.

  • Abstract

    This article introduces a two-parameter probability model which represents another generalization of the Inverse Exponential distribution by using the quadratic rank transmuted map. The proposed model is named Transmuted Inverse Exponential (TIE) distribution and its statistical properties are systematically studied. We provide explicit expressions for its moments, moment generating function, quantile function, reliability function and hazard function. We estimate the parameters of the TIE distribution using the method of maximum likelihood estimation (MLE). The hazard function of the model has an inverted bathtub shape and we propose the usefulness of the TIE distribution in modeling breast cancer and bladder cancer data sets.

    Author Biography

    • Pelumi Oguntunde, Covenant University
      Department of Mathematics

  • References

    1. [1] Ahmad A., Ahmad S. P., and Ahmed A. “Transmuted Inverse Rayleigh Distribution: A Generalization of the Inverse Rayleigh Distributionâ€, Mathematical Theory and Modeling, Vol. 4, No. 7, 2014.

      [2] Aryal G. R., Tsokos C. P. “Transmuted Weibull Distribution: A Generalization of the Weibull Probability Distributionâ€, European Journal of Pure and Applied Mathematics, Vol. 4, No. 2, 2011, 89-102.

      [3] Ashour S. K., and Eltehiwy M. A. “Transmuted Exponentiated Modified Weibull Distributionâ€, International journal of Basic and Applied Sciences, 2013a, Vol 2(3) 258-269.

      [4] Ashour S. K., and Eltehiwy M. A. “Transmuted Lomax Distributionâ€, American Journal of Applied Mathematics and Statistics, 2013b, Vol. 1, No. 6, 121-127. http://dx.doi.org/10.12691/ajams-1-6-3.

      [5] Elbatal I. “Transmuted Modified Inverse Weibull Distribution: A Generalization of the Modified Inverse Weibull Probability Distribution†International Journal of Mathematical Archive, 4 (8), 2013, 117-129.

      [6] Hussian M. A. “Transmuted Exponentiated Gamma Distribution: A Generalization of the Exponentiated Gamma Probability Distributionâ€, Applied Mathematical Sciences, Vol. 8, 2014, No. 27, 1297-1310.

      [7] Keller, A. Z and Kamath, A. R (1982). “Reliability analysis of CNC Machine Toolsâ€. Reliability Engineering. Vol. 3, pp. 449-473. http://dx.doi.org/10.1016/0143-8174(82)90036-1.

      [8] Khan M. S., King R. and Hudson I. L. “Characteristics of the transmuted inverse weibull distributionâ€, ANZIAM J. 55 (EMAC2013) pp. C197-C217, 2014.

      [9] Lin, C. T, Duran, B. S and Lewis, T. O. “Inverted Gamma as life distributionâ€. Microelectron Reliability, Vol. 29 (4), (1989) 619-626. http://dx.doi.org/10.1016/0026-2714(89)90352-1.

      [10] Merovci, F., “Transmuted Rayleigh Distributionâ€, Austrian Journal of Statistics, Vol. 42 (1), 21-31, 2013

      [11] Merovci F., Puka L., “Transmuted Pareto Distributionâ€, ProbStat Forum, Volume 07, January 2014, Pages 1-11.

      [12] Oguntunde P. E., Babatunde O. S., and Ogunmola A. O., “Theoretical Analysis of the Kumaraswamy-Inverse Exponential Distribution†International Journal of Statistics and Applications, Vol. 4, No. 2, (2014), 113-116.

      [13] Oguntunde P. E., Odetunmibi O. A., & Adejumo A. O., “A Study of Probability Models in Monitoring Environmental Pollution in Nigeria,†Journal of Probability and Statistics, vol. 2014, Article ID 864965, 6 pages, 2014. doi:10.1155/2014/864965. http://dx.doi.org/10.1155/2014/864965.

      [14] Oguntunde, P. E, Odetunmibi, O. A., Adejumo A. O. “On the Sum of exponentially distributed random variables: A convolution approachâ€. European Journal of Statistics and Probability, 2(1), 1-8, 2014. http://dx.doi.org/10.1155/2014/864965.

      [15] Oguntunde P. E, Odetunmibi O. A, Edeki S. O, Adejumo A. O., “On the modified ratio of exponential distributions†Bothalia Journal, vol 44, no 4, pp. 166-174, 2014.

      [16] Shaw W and Buckley, I. (2007).The alchemy of probability distributions: beyond Gram- Charlier expansions and a skew- kurtotic- normal distribution from a rank transmutation map. Research Report, 2007.

      [17] Singh S. K., Singh U., Kumar M. “Estimation of Parameters of Generalized Inverted Exponential Distribution for Progressive Type-II Censored Sample with Binomial Removalsâ€. Journal of Probability and Statistics. Volume 2013, Article ID 183652. http://dx.doi.org/10.1155/2013/183652.

  • Downloads

  • Received date: 2014-10-06

    Accepted date: 2014-11-02

    Published date: 2014-12-12