Marshall-Olkin Half Logistic Distribution with Theory and Applications

Abstract

In this study we present a new distribution named as Marshall-Olkin Half Logistic (MOHL) by extending half logistic distribution to increase the flexibility. We derive some fundamental properties including survival function, hazard rate function, skewness, kurtosis, order statistics and entropy function. Parameters are estimated using maximum likelihood estimation method to fit new model. Then, a simulation study is conducted to show the performance of the proposed model.

Keywords

• Half logistic distribution,Maximum likelihood estimation,Simulation,Entropy

Teori ve Uygulamaları ile Marshall-Olkin Yarı Lojistik Dağılımı

Öz

Bu çalışmada esnekliği arttırmak için yarı lojistik dağılımı genişletilerek yeni bir dağılım olarak Marshall-Olkin Yarı Lojistik (MOYL) dağılımı önerilmiştir. Yaşam fonksiyonu, tehlike oranı fonksiyonu, çarpıklık, basıklık, sıralı istatistikler ve entropi fonksiyonu gibi temel özellikler elde edilmiştir. Yeni modelin uyumu için en çok olabilirlik yöntemi kullanılmıştır Daha sonra önerilen modelin performansı için bir simülasyon çalışması yapılmıştır.

Anahtar Kelimeler

• Yarı Lojistik Dağılımı,En Çok Olabilirlik Tahmini,Simülasyon,Entropi,Sıralı İstatistik

References

1. Balakrishnan, N. Order statistics from the Half Logistic Distribution. Journal of Statistical Computation and Simulation, 287-309, 1985.Balakrishnan, N. and Puthenpura, S. Best Linear Unbiased Estimators of Location and Scale Parameters of the Half Logistic Distribution. Journal of Statistical Computation and Simulation, 193-204, 1986.Balakrishnan, N. and Wong, K.H.T., Approximate MLEs for the Location and Scale Parameters of the Half-Logistic Distribution with Type-II Right-Censoring. IEEE Transactions on Reliability, 40(2), 140-145, 1991.Caroni, C. Testing for the Marshall-Olkin extended form of the Weibull distribution. Statistical Papers, 51: 325-336, 2010.Economou, P. and Caroni, C. Parametric proportional odds frailty models. Communication in Statistics Simulation and Computation, 36: 579-592, 2007.Cordeiro, G.M., Alizadeh, M. and Ortega, E.M.M. The exponentiated half logistic family of distributions: Properties and applications. Journal of Probability and Statistics, 2014.Cordeiro, G.M., Alizadeh, M. and Marinho, P.R.D. The type I half-logistic family of distributions. Journal of Statistical Computation and Simulation, 86(4):707-728, 2016.Ghitany, M.E., Al-Hussaini, E.K. and Al-Jarallah, R.A. Marshall-Olkin extended Weibull distribution and its application to censored data. Journal of Applied Statistics, 32: 1025-1034, 2005a.Ghitany, M.E. Marshall-Olkin extended Pareto distribution and its application. Int J Appl Math 18: 17-32, 2005b.Ghitany, M.E, Al-Awadhi, F.A. and Alkhalfan, L.A. Marshall-Olkin extended Lomax distribution and its application to censored data. Communication in Statistics : Theory and Methods, 36: 1855-1866, 2007.Ghitany, ME and Kotz, S. Reliability properties of extended linear failure-rate distributions. Probab Eng Inform Sc 21: 441-450, 2007.Gómez-Déniz, E. Another generalization of the geometric distribution. Test, 19: 399-415, 2010.Gupta, R.D. and Peng, C. Estimating reliability in proportional odds ratio models. Computational Statistics and Data Analysis, 53: 1495-1510, 2009.Gupta, R.C., Lvin, S. and Peng, C. Estimating turning points of the failure rate of the extended Weibull distribution. Computational Statistics and Data Analysis, 54: 924-934, 2010.Kenney, J.F., Mathematics of Statistics, London: Chapman & Hall, 1939.Krishnarani, S.D. On a power transformation of half-logistic distribution. Journal of Probability and Statistics, 2016.Lam, K.F. and Leung, T.L., Marginal likelihood estimation for proportional odds models with right censored data. Lifetime Data Analysis, 7: 39-54, 2001.Marshall, A.W. and Olkin I., A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84: 641-652, 1997.Moors, J.J.A., A quantile alternative for kurtosis, Statistician, 37, 1, 25–32, 1988.Nanda, A.K. and Das, S. Stochastic orders of the Marshall-Olkin extended distribution. Statistics and Probability Letters, 82: 295-302, 2012. Olapade, A.K., On Characterizations of the Half Logistic Distribution. InterStat, February Issue,2, http://interstat.stat.vt.edu/InterStat/ARTICLES/2003articles/F06002.pdf, 2003.Olapade A.K., The type I generalized half logistic distribution. Journal of the Iranian Statistical Society, 13(1):69-82, 2014.Ristić, M.M., Jose, K.K. and Ancy, J., A Marshall-Olkin gamma distribution and minification process. STARS: Stress and Anxiety Research Society 11: 107-117, 2007.Torabi, H. and Bagheri, F.L. Estimation of Parameters for an Extended Generalized Half Logistic Distribution Based on Complete and Censored Data. JIRSS, 9(2), 171-195, 2010.Zhang, T. and Xie, M,. Failure data analysis with extended Weibull distribution. Communication in Statistics: Simulation and Computation, 36: 579-592, 2007.