The Kumaraswamy Pareto distribution
Tóm tắt
The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. For the first time, the called Kumaraswamy Pareto distribution, is introduced and studied. The new distribution can have a decreasing and upside-down bathtub failure rate function depending on the values of its parameters. It includes as special sub-models the Pareto and exponentiated Pareto (Gupta et al., 1998) distributions. Some structural properties of the proposed distribution are studied including explicit expressions for the moments and generating function. We provide the density function of the order statistics and obtain their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. A real data set is used to compare the new model with widely known distributions.
Tài liệu tham khảo
Akinsete, A., Famoye, F. and Lee, C. (2008). The beta-Pareto distribution. Statistics, 42, 6, 547–563.
Barreto-Souza, W., Santos, A.H.S. and Cordeiro, G.M.(2010). The beta generalized exponential distribution. Journal of Statistical Computation and Simulation, 80, 159–172.
Choulakian, V. and Stephens, M.A. (2001). Goodness-of-fit for the generalized Pareto distribution. Technometrics, 43, 478–484.
Cordeiro G. M. and de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81, 883–898.
Cordeiro, G.M., Ortega, E.M.M. and Nadarajah, S. (2010). The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute, 347, 1399–1429.
Cordeiro, G.M., Nadarajah, S. and Ortega, E.M.M. (2012). The Kumaraswamy Gumbel distribution. Statistical Methods and Applications, 21, 139–168.
Eugene, N., Lee, C. and Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics: Theory and Methods, 31, 497–512.
Gupta, R.D. and Kundu, D. (2001). Exponentiated exponential distribution: An alternative to gamma and Weibull distributions. Biomet. J., 43, 117–130.
Gupta, R.C., Gupta, R.D. and Gupta, P.L. (1998). Modeling failure time data by Lehman alternatives. Communications in Statistics: Theory and Methods, 27, 887–904.
Hogg, R.V., McKean, J.W. and Craig, A.T. (2005). Introduction to Mathematical Statistics, 6th ed. Pearson Prentice-Hall, New Jersey, 2005.
Jones, M. C. (2009). A beta-type distribution with some tractability advantages. Statistical Methodology, 6, 70–81.
Keeping E.S. Kenney, J.F. (1962). Mathematics of Statistics. Part1.
Kumaraswamy, P. (1980). Generalized probability density-function for double-bounded random-processes. Journal of Hydrology, 462, 79–88.
Kundu, D. and Raqab, M.Z. (2005). Generalized Rayleigh distribution: Different methods of estimation. Comput. Statist. Data Anal., 49, 187–200.
Mahmoudi, E. (2011). The beta generalized Pareto distribution with application to lifetime data. Mathematics and Computers in Simulation, 81, 11, 2414–2430.
Moors, J.J. (1998). A quantile alternative for kurtosis. Journal of the Royal Statistical Society D, 37, 25–32.
Nadarajah, S., Cordeiro, G.M. and Ortega, E.M.M. (2011). General results for the Kumaraswamy-G distribution. Journal of Statistical Computation and Simulation. DOI: https://doi.org/10.1080/00949655.2011.562504.
Pascoa, A.R.M., Ortega, E.M.M. and Cordeiro, G.M. (2011). The Kumaraswamy generalized gamma distribution with application in survival analysis. Statistical Methodology, 8, 411–433.
Pickands, J. (1975). Statistical inference using extreme order statistics. Annals of Statistics, 3, 119–131.
Saulo, H., Leão, J. and Bourguignon, M. (2012). The Kumaraswamy Birnbaum-Saunders Distribution. Journal of Statistical Theory and Practice, 6, 745–759.
Silva, G.O., Ortega, E.M.M. and Cordeiro, G.M. (2010). The beta modified Weibull distribution. Lifetime Data Anal, 16, 409–430.
Silva, R.B., Barreto-Souza, W. and Cordeiro, G.M. (2010). A new distribution with decreasing, increasing and upside-down bathtub failure rate. Comput. Statist. Data Anal., 54, 935–934.