Novel Weighted G family of Probability Distributions with Properties, Modelling and Different Methods of Estimation
Abstract
In this work, we derive and study a new weighted G family of continuous distributions called the new weighted generated family (NW-G). We study some basic properties including quantile function, asymptotic, the mixture for CDF and pdf, residual entropy, and order statistics. Then, we study half-logistic distribution as a special case with more details. Comprehensive graphical simulations are performed under some common estimation methods. Finally, two real-life data sets are analyzed to demonstrate the objectives.References
Alexander, C., Cordeiro, G. M., Ortega, E. M., Sarabia, J. M. (2012). Generalized beta-generated distributions. Computational Statistics Data Analysis, 56(6), 1880-1897.
Alizadeh, M., Emadi, M., Doostparast, M. (2019). A new two-parameter lifetime distribution: properties, applications and different method of estimations. Statistics, Optimization Information Computing, 7(2), 291-310.
Alizadeh, M., Afshari, M., Hosseini, B., Ramires, T. G. (2018). Extended exp-G family of distributions: Properties, applications and simulation.Communications in Statistics-Simulation and Computation, 1-16.
Anderson, T. W. and Darling, D. A. (1952). Asymptotic theory of certain ”goodness of fit” criteria based on stochastic processes. The annals of mathematical statistics, 193-212.
Balakrishnan, N. (1985). Order statistics from the half logistic distribution. Journal of Statistical Computation and Simulation, 20(4), 287-309.
Cheng RCH, Amin NAK (1979) Maximum product-of-spacings estimation with applications to the lognormal distribution. Technical Report, Department of Mathematics, University of Wales
Cheng RCH, Amin NAK (1983) Estimating parameters in continuous univariate distributions with a shifted origin. J R Stat Soc B3:394-403.
Choi, K. and Bulgren, W. (1968). An estimation procedure for mixtures of distributions. Journal of the Royal Statistical Society. Series B (Methodological), 444-460.
Cordeiro, G. M., de Castro, M. (2011). A new family of generalized distributions. Journal of statistical computation and simulation, 81(7), 883-898.
Cordeiro, G. M., Ortega, E. M., da Cunha, D. C. (2013). The exponentiated generalized class of distributions. Journal of data science, 11(1), 1-27.
Dey, S., Mazucheli, J., Nadarajah, S. (2017). Kumaraswamy distribution: different methods of estimation. Computational and Applied Mathematics, 1-18.
Ghitany, M. E., Atieh, B., Nadarajah, S. (2008). Lindley distribution and its application. Mathematics and computers in simulation, 78(4), 493-506.
Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan, N., Al-Enezi, L. J. (2013). Power Lindley distribution and associated inference. Computational Statistics Data Analysis, 64, 20-33.
Gupta, R. C., Gupta, P. L., Gupta, R. D. (1998). Modelling failure time data by Lehman alternatives. Communications in StatisticsTheory and methods, 27(4), 887-904.
Gupta, R. D., Kundu, D. (1999). Theory methods: Generalized exponential distributions. Australian New Zealand Journal of Statistics, 41(2), 173-188.
Jones, M. C. (2004). Families of distributions arising from distributions of order statistics. Test, 13(1), 1-43.
Kang, S. B., Seo, J. I. (2011). Estimation in an exponentiated half logistic distribution under progressively type-II censoring. Communications for Statistical Applications and Methods, 18(5), 657-666.
Leadbetter, M. R., Lindgren, G., Rootz´en, H. (2012). Extremes and related properties of random sequences and processes. Springer Science Business Media.
Lehmann, E. L. (1953). The power of rank tests. The Annals of Mathematical Statistics, 23-43.
Murthy, D. P., Xie, M., Jiang, R. (2004). Weibull models Vol. 505. John Wiley Sons.
Nadarajah, S., Bakouch, H. S., Tahmasbi, R. (2011). A generalized Lindley distribution.Sankhya B, 73(2), 331-359.
Oliveira, J., Santos, J., Xavier, C., Trindade, D., Cordeiro, G. M. (2016). The McDonald half-logistic distribution: Theory and practice.Communications in Statistics-Theory and Methods, 45(7), 2005-2022.
Patil, G. P., Rao, C. R., Ratnaparkhi, M. V. (1986). On discrete weighted distributions and their use in model choice for observed data. Communications in Statistics-Theory and Methods, 15(3), 907-918.
Swain, J. J., Venkatraman, S., and Wilson, J. R. (1988). Least-squares estimation of distribution functions in johnson’s translation system. Journal of Statistical Computation and Simulation, 29, 271- 297.
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