A Study on Transmuted Half Logistic Distribution: Properties and Application
Adeyinka Femi Samuel, Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
Olapade Akintayo Kehinde, Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
Received: May 2, 2019; Accepted: Jun. 24, 2019; Published: Aug. 13, 2019
In this article we transmute the half logistic distribution using quadratic rank transmutation map to develop a transmuted half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its 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 transmuted half logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the transmuted half 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 function of the transmuted half logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. 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 transmuted half 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 the literature in fitting positive real data.
Half Logistic Distribution, Reliability Function, Hazard Rate Function, Parameter Estimation, Order Statistics, Transmutation
Adeyinka Femi Samuel, Olapade Akintayo Kehinde, A Study on Transmuted Half Logistic Distribution: Properties and Application, International Journal of Statistical Distributions and Applications. Vol. 5, No. 3, 2019, pp. 54-59. doi: 10.11648/j.ijsd.20190503.12
Balakrishnan N. (1985). Order Statistics from the half logistic distribution. Journal of Statistical Computation and Simulation. 20 (4): 287-309.
Balakrishnan N., and Puthenpura, S. (1986). Best linear unbiased estimators of location and scale parameters of the half logistic distribution. Journal of Statistical Computation and Simulation., 25, 193-204.
Balakrishnan N., Wong K. H. T (1991). Approximate MLEs for the Location and Scale Parameters of Half-Logistic Distribution with Type-II Right-Censoring. IEE Transactions on Reliability. 40 (2), 140-145.
Olapade, A. K. (2003). On Characterizations of the Half Logistic Distribution. InterStat, Feburary Issue, 2, http://interstat.stat.vt.edu/InterStat/ARTICLES/2003articles/F06002.pdf
Torabi, H, and Bagheri, F. L. (2010). Estimation of Parameters for an Extended Generalized Half Logistic Distribution Based on Complete Censored Data. JIRSS, 9 (2), 171-195.
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.
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.
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.
Rahman M. M, Al-Zahrani B, Shahbaz M. Q (2018). A general transmuted family of distributions. Pak J Stat Oper Res 14:451-469.
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.
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.