An extended version of inverse Weibull distribution: properties and application / Uma versão ampliada da distribuição Weibull inversa: propriedades e aplicação
DOI:
https://doi.org/10.34117/bjdv8n7-162Keywords:
hazard function, Kumaraswamy distribution, maximum likelihood estimation, Weibull distribution, characterizations, survival analysis.Abstract
In this paper, we propose lifetime model which is obtained from the inverse Weibull distribution and the exponentiated Kumaraswamy. The presented distribution includes as special cases the inverse exponential, inverse Weibull, inverse Rayleigh and exponentiated inverse Weibull distributions. We study the main properties of this distribution, with special emphasis on its moments and some characteristics related to reliability studies. We also discuss parameter estimation considering the methods of moments and maximum likelihood. An application reveals that the model proposed can be very useful in fitting real data.
References
B.C. Arnold, A.N. Balakrishnan, and H.N. Nagaraja, A first course in order statistics, Wiley-Interscience, New York, 1992.
L.A. Baharith, S.A. Mousa, M.A. Atallah and S.H. Elgayar, The beta generalized inverse Weibull distribution, British Journal of Mathematics and Computer Science. 4 (2014), pp. 252–270.
W. Glänzel, A characterization theorem based on truncated moments and its application to some distribution families, Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Vol. B, Reidel, Dordrecht, 1987, pp. 75–84.
A.J. Gross and V.A. Clark, Survival distributions: Reliability applications in the biomedical sciences, Wiley-Interscience, New York, 1975.
F.R.S. Gusmão, E.M.M. Ortega and G.M. Cordeiro, The generalized inverse Weibull distribution, Statistical Papers. 52 (2011), pp. 591–619.
G.G. Hamedani, On certain generalized gamma convolution distributions II, Technical Report, No. 484, MSCS, Marquette University (2013).
S. Huang and B.O. Oluyede, Exponentiated Kumaraswamy-Dagum distribution with applications to income and lifetime data, Journal of Statistical Distributions and Applications. 1 (8) (2014), pp. 1–18.
A.Z. Keller and A.R. Kamath, Reliability analysis of CNC Machine Tools, Reliability Engineering. 3 (6) (1982), pp. 449–473.
M.S. Khan and R. King, Modified inverse Weibull distribution, Journal of Statistics Applications and Probability. 1(2) (2012), pp. 115–132.
M.S. Khan, The beta inverse Weibull distribution, International Transactions in Mathematical Sciences and Computer. 3 (2010), pp. 113–119,
P. Kumaraswamy, A generalized probability density function for double-bounded random processes, Journal of Hydrology. 46 (1980), pp. 79–88.
A.J. Lemonte, W.B. Souza and G.M. Cordeiro, The exponentiated Kumaraswamy distribution and its log-transform, Brazilian Journal of Probability and Statistics. 27(1) (2013), pp. 31–53.
M.Q. Shahbaz, S. Shahbaz and N.S. Butt, The Kumaraswam-Inverse Weibull Distribution, Statistics in the Twenty-First Century. 8 (2012), pp. 479–489.
V.G. Vodã, On the Inverse Rayleigh Distribution Random Variable, Rep Statistical Applied Research JUSE. 19 (1972), pp. 13–21.

