Transmuted Modified Inverse Rayleigh Distribution
AbstractWe introduce the transmuted modified Inverse Rayleigh
distribution by using quadratic rank transmutation map (QRTM), which
extends the modified Inverse Rayleigh distribution. A comprehensive
account of the mathematical properties of the transmuted modified Inverse
Rayleigh distribution are discussed. We derive the quantile, moments,
moment generating function, entropy, mean deviation, Bonferroni and
Lorenz curves, order statistics and maximum likelihood estimation The
usefulness of the new model is illustrated using real lifetime data.
Ammar M. Sarhan and Mazen Zaindin. Modified Weibull distribution, Applied Sciences, 11, 123-136, 2009.
Balakrishnan AN, Nagaraja HN. A first course in order statistics. New York: Wiley-Interscience; 1992.
Bonferroni C.E. Elmenti di statistica generale. Libreria Seber, Firenze, 1930.
Gauss M. Cordeiro, Antonio Eduardo Gomes , Cibele Queiroz da-Silva, Edwin M. M. Ortega. The beta exponentiated Weibull distribution, Journal of Statistical Computation and Simulation. 83,1, 114–138, 2013.
Gharraph, M.K. Comparison of Estimators of Location Measures of an Inverse Rayleigh Distribution. The Egyptian Statistical Journal. 37, 295-309, 1993.
Gokarna R. Aryal1, Chris P. Tsokos. On the transmuted extreme value distribution with applications. Nonlinear Analysis: Theory, Methods and applications, Vol. 71, 1401-1407, 2009.
Gokarna R. Aryal1, Chris P. Tsokos. Transmuted Weibull distribution: A Generalization of the Weibull Probability Distribution. European Journal of Pure and Applied Mathematics, Vol. 4, No. 2, 2011, 89-102, 2011.
Hinkley, D. On quick choice of power transformations. The American Statistician, 26, 67-69, 1977.
J. F. Kenney and E. S. Keeping. Mathematics of Statistics. Princeton, NJ, 1962.
Khan, M.S, Modified Inverse Rayleigh Distribution. International Journal of Computer Applications, 87(13):28-33, February 2014.
Khan, M.S, King Robert, Transmuted Modified Weibull Distribution: A Generalization of the Modified Weibull Probability Distribution, European Journal of Pure And Applied Mathematics, Vol. 6, No. 1, 66-88, 2013.
Khan, M. Shuaib, King Robert. Transmuted Generalized Inverse Weibull Distribution, Journal of Applied Statistical Sciences, Nova Science. Vol. 20 (3), 15-32, 2013.
Khan, M.S, King Robert, Hudson Irene, Transmuted Generalized Exponential Distribution, 57th Annual Meeting of the Australian Mathematical Society, September 30-October 3, 2013 at the University of Sydney, Australia.
Khan, M.S, King Robert. Modified Inverse Weibull Distribution, J. Stat. Appl. Pro. 1, No. 2, 115-132, 2012.
Khan, M.S, Pasha, G.R and Pasha, A.H. Theoretical analysis of Inverse Weibull distribution. WSEAS Transactions on Mathematics, 7(2), 30-38, 2008.
Lorenz, M. O. "Methods of measuring the concentration of wealth". The American Statistical Association, Vol. 9, No. 70) 9 (70): 209–219, 1905.
Mohsin and Shahbaz. Comparison of Negative Moment Estimator with Maximum Likelihood Estimator of Inverse Rayleigh Distribution, PJSOR, Vol.1: 45-48, 2005.
Mukarjee, S.P. and Maitim, S.S. A Percentile Estimator of the Inverse Rayleigh Parameter. IAPQR Transactions, 21, 63-65, 1996.
Merovci, F. Transmuted Rayleigh distribution. Austrian Journal of Statistics, Volume 42, Number 1, 21-31, 2013.
Trayer, V. N. Doklady Acad, Nauk, Belorus, U.S.S.R, 1964.
Voda, V. Gh. On the Inverse Rayleigh Random Variable, Pep.
Statist. App. Res., JUSE, 19, 13-21, 1972.
W. Shaw and I. Buckley. The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. arXiv preprint arXiv:0901.0434, 2009.
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