International Journal of Statistical Distributions and Applications
Volume 5, Issue 2, June 2019, Pages: 32-37
Received: May 5, 2019;
Accepted: Jun. 5, 2019;
Published: Jul. 16, 2019
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Femi Samuel Adeyinka, Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
Akintayo Kehinde Olapade, Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
In this article we transmute the four parameters generalized log-logistic distribution using quadratic rank transmutation map to develop a transmuted four parameters generalized log-logistic distribution. The quadratic rank transmutation map helps to introduce extra parameter into the baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the four parameters generalized log-logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the four parameters generalized log-logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density functions of the four parameters generalized log-logistic distribution are considered. The parameter estimation is done by the maximum likelihood method. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the four parameters generalized log-logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in fitting positive real data.
Femi Samuel Adeyinka,
Akintayo Kehinde Olapade,
On Transmuted Four Parameters Generalized Log-Logistic Distribution, International Journal of Statistical Distributions and Applications.
Vol. 5, No. 2,
2019, pp. 32-37.
Shah, B. K., and Dave, P. H. (1963). A note on log-logistic distribution. Journal of Mathematical Sciences of University of Baroda. Vol 12. Pp 21-22.
Tadikamalla, P. R., and Johnson, N. L. (1982). Systems of frequency curves generated by the transformation of logistic variables. Biometrika. Vol 69. Pp 461 465.
O’Quigley, J., and Struthers, L. (1982). Survival model based upon the logistic and log-logistic distribution. Computer programmes in Biomedicine. Vol 15. Pp 3-12.
Ragab, A., and Green, J. (1984). On order statistics from the log-logistic distribution and their properties. Communications in statistics-Theory and Methods. Vol 13. Pp 2713-2724.
Balakrishnan, N., Malik, H. J., and Puthenpura, S. (1987): Best linear unbiased estimation of location and scale parameters of the log-logistic distribution. Communications in Statistics-Theory and Methods. Vol 12. Pp 3477-3495.
Aryal, G. R. (2013). Transmuted log-logistic distribution. Journal of Statistics Applications and probability. 2 (1), 11-20.
Olapade, A. K. (2010). On log-logistic and a four-parameter generalized log-logistic distributions. Proceedings of the Jangjeon Mathematical Society. Vol 13. Pp 67-76.
Usman, R. M, Haq, M. A and Talib, J (2017). Kumaraswamy Half-Logistic Distribution: Properties and Applications. Journal of Statistics Applications and Probability. No 3,597-609.
Aryal, G. R, and Tsokos, C. P. (2009). On the transmuted extreme value distribution with application. Nonlinear Analysis: Theory, Methods and Application.71 (12), el401-el407.
Aryal, G. R, and Tsokos, C. P. (2011). Transmuted Weilbull distribution: A generalization of Weilbull probability distribution. European Journal of Pure and Applied Mathematics. 4 (2), 89-102.
Bjerkedal, T (1960). Acquisition of Resistance in Guinea Pigs infected with Different Doses of Virulent Tubercle Bacilli, American Journal of Hygiene, 72, 130-148.
Granzoto, D. C. T., Louzada, F., and Balakrishnan, N. (2017). Cubic rank transmuted distributions: Inferential issues and applications. Journal of statistical Computation and Simulation. 87: 2760-2778, doi. 10-1080/00949655.2017.1344239.
Haq, M. A, (2016). Kumaraswamy Exponentiated Inverse Rayleigh Distribution.
Merovci, F., Alizadeh, M., and Hamedani, G. (2016). Another Generalized Transmuted Family of Distributions: Properties and Applications. Austrian Journal of Statistics. 45, 71-93.
Merovci, F. (2014). Transmuted Generalized Rayleigh Distribution. Journal of Statistics Applications and Probability. 3 (1), 9-20.
Merovci, F., Elbatal, I. (2014). Transmuted Lindley-geometric Distribution and its Applications. Journal of Statistics Applications and Probability. 3 (1), 77-91.
Merovci, F., Puka, L. (2014). Transmuted Pareto Distribution. Probstat.7, 1-11.
Olapade, A. K. (2003). On the type I generalized logistic, log-logistic and generalized log-logistic distributions. Proceedings of the Jangjeon Mathematical Society. Vol 6. Pp 137-146.
Rahman M. M, Al-Zahrani B, Shahbaz M. Q (2018). A general transmuted family of distributions. Pak J Stat Oper Res 14: 451-469.
Shaw, W. T, and Buckley, I. R. (2009). Alchemy of Probability Distributions: Beyond Gram-Charlier and Cornish -Fisher Expansions, and Skewed- kurtotic Normal Distribution from a Rank Transmutation Map. arxivpreprint arxiv: 0901.0434.