A new flexible generalized family for constructing many families of distributions.(English)Zbl 1528.62011
Summary: We propose anew flexible generalized family (NFGF) for constructing many families of distributions. The importance of the NFGF is that any baseline distribution can be chosen and it does not involve any additional parameters. Some useful statistical properties of the NFGF are determined such as a linear representation for the family density, analytical shapes of the density and hazard rate, random variable generation, moments and generating function. Further, the structural properties of a special model named thenew flexible Kumaraswamy (NFKw) distribution, are investigated, and the model parameters are estimated by maximum-likelihood method. A simulation study is carried out to assess the performance of the estimates. The usefulness of the NFKw model is proved empirically by means of three real-life data sets. In fact, the two-parameter NFKw model performs better than three-parameter transmuted-Kumaraswamy, three-parameter exponentiated-Kumaraswamy and the well-known two-parameter Kumaraswamy models.
MSC:
| 62E15 | Exact distribution theory in statistics |
Keywords:
flexible G-family;generalized family;Kumaraswamy distribution;maximum-likelihood method;new flexible family;T-X familyCite
References:
| [1] | Ahmad, Z.; Elgarhy, M.; Hamedani, G. G., A new Weibull-X family of distributions: properties, characterizations and applications, J. Stat. Distrib. Appl., 5, 18 (2018) ·Zbl 1420.60012 |
| [2] | Alzaatreh, A.; Famoye, F.; Lee, C., A new method for generating families of continuous distributions, Metron, 71, 63-79 (2013) ·Zbl 1302.62026 |
| [3] | Cordeiro, G. M.; Ortega, E. M.M.; Cunha, D. C.C., The exponentiated generalized class of distributions, J. Data Sci., 11, 1-27 (2013) |
| [4] | Eugene, N.; Lee, C.; Famoye, F., Beta-normal distribution and its applications, Commun. Stat. Theory Methods, 31, 497-512 (2002) ·Zbl 1009.62516 |
| [5] | Gleaton, J. U.; Lynch, J. D., Properties of generalized log-logistic families of lifetime distributions, J. Probab. Stat. Sci., 4, 51-64 (2006) |
| [6] | Granzotto, D. C.T.; Louzada, F.; Balakrishnan, N., Cubic rank transmuted distributions: inferential issues and applications, J. Stat. Comput. Simul., 87, 2760-2778 (2016) ·Zbl 1492.62044 |
| [7] | Gupta, R. C.; Gupta, P. L.; Gupta, R. D., Modeling failure time data by Lehman alternatives, Commun. Stat. Theory Methods, 27, 887-904 (1999) ·Zbl 0900.62534 |
| [8] | Khan, M. S.; King, R.; Hudson, L. I., Transmuted Kumaraswamy distribution, Stat. Trans., 17, 183-210 (2016) |
| [9] | Lee, C.; Famoye, F.; Alzaatreh, A., Methods for generating families of univariate continuous distributions in the recent decades, WIREs Comput. Stat., 5, 219-238 (2013) ·Zbl 1540.62014 |
| [10] | Lemonte, A. J.; Barreto-Souza, W.; Cordeiro, G. M., The exponentiated Kumaraswamy distribution and its log-transform, Braz. J. Probab. Stat., 27, 31-53 (2013) ·Zbl 1319.62032 |
| [11] | Marshall, A. W.; Olkin, I., A new method for adding parameters to a family of distributions with application to the exponential and Weibull families, Biometrika, 84, 641-652 (1997) ·Zbl 0888.62012 |
| [12] | Shaw, W.T. and Buckley, I.R., The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, UCL discovery repository (2007). Available at http://discovery.ucl.ac.uk/id/eprint/643923. |
| [13] | Tahir, M. H.; Cordeiro, G. M., Compounding of distributions: a survey and new generalized classes, J. Stat. Distrib. Appl., 3, 13 (2016) ·Zbl 1375.60050 |
| [14] | Tahir, M. H.; Cordeiro, G. M.; Alizadeh, M.; Mansoor, M.; Zubair, M., The logistic-X family of distributions and its applications, Commun. Stat. Theory Methods, 45, 7326-7349 (2016) ·Zbl 1349.60017 |
| [15] | Tahir, M. H.; Nadarajah, S., Parameter induction in continuous univariate distributions: well-established G families, An. Acad. Bras. Ciênc., 87, 539-568 (2015) |
| [16] | Torabi, H.; Montazari, N. H., The logistic-uniform distribution and its application, Commun. Stat. Simul. Comput., 43, 2551-2569 (2014) ·Zbl 1462.62110 |
| [17] | Zografos, K.; Balakrishnan, N., On families of beta- and generalized gamma generated distributions and associated inference, Stat. Methodol., 6, 344-362 (2009) ·Zbl 1463.62023 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
