The beta transmuted dagum distribution: theory and applications
- 1Department of Statistics, Sana'a University, Yemen
Res. J. Mathematical & Statistical Sci., Volume 8, Issue (2), Pages 5-11, May,12 (2020)
In this paper, we introduce a new family of continuous distributions called the beta transmuted Dagum distribution which extends the beta and transmuted family. The density function, hazard function, shape of the density and hazard functions, moments, moment generating function, quantiles and stress-strength of the beta transmuted Dagum distribution(BTD) are provided and discussed in detail. We discuss the maximum likelihood estimation of the model parameters. We assess the performance of the maximum likelihood estimators in terms of biases, standard errors, and mean square of errors by means of simulation studies. The usefulness of the new model is illustrated through an application to survival dataset.
- Dagum, C. (1977)., A new model of personal income distribution: speciﬁcation and estimation., Economie Appliquee., 30(3), 413-437.
- Dagum, C. (1980)., The generation and distribution of income, the Lorenz curve and the Gini ratio., Economie Appliquée., 33, 327-367.
- Dagum, C. (1996)., A systematic approach to the generation of income distribution models., Journal of Income Inequality, 6, 105-126.
- Dagum, C. (2006)., Wealth distribution models: Analysis and applications., Statistica, 16, 235-268.
- Costa, M. (2006)., The Dagum model of human capital distribution., Statistica, 66(3), 313-324.
- Pérez, C.G., and Alaiz, M.P. (2011)., Using the Dagum model to explain changes in personal income distribution., Applied Economics, 43(28), 4377-4386.
- Ivana, M. (2011)., Distribution of incomes per capita of the Czech households from 2005 to 2008., Journal of Applied Mathematics, 4, 305-310.
- Lukasiewicz, P., Karpio, K., and Orlowski, A. (2012)., The models of personal income in USA., Acta Physica Polonica., A121, B82-B85.
- Binoti, D.H.B., Binoti, M.L.M.S., Leite, H.G., Fardin, L. and Oliveira, J.C. (2012)., Probability density functions for description of diameter distribution in thinned stands of Tectona grandis., Cerne., 18, 185-196.
- Alwan, F.M., Baharum, A. and Hassan, G.S. (2013)., Reliability measurement for mixed mode failures of 33/11 kilovolt electric power distribution stations., PLOS ONE., 8, 1-8.
- Christian Kleiber & Samuel Kotz (2003)., Statistical Size Distributions in Economics and Actuarial Sciences., A john Wiley and Sons, Inc., publication., New York, pp183-230. ISBN: 0-471-15064-9 (cloth)
- Shehzad, M.N. and Asghar, Z. (2013)., Comparing TL-moments, L-moments and conventional moments of Dagum distribution by simulated data., Colombian Journal of Statistics., 36(1), 79-93.
- Pant, M.D. and Headrick, T.C. (2013)., An L-moment based characterization of the family of Dagum distributions., Journal of Statistical and Econometric Methods, 2, 17-30.
- Domma, F. (2007)., Asymptotic distribution of the maximum likelihood estimators of the parameters of the right-truncated Dagum distribution., Communications in Statistics-Simulation and Computation, 36, 1187-1199.
- Pollastri, A. and Zambruno, G. (2010)., Distribution of the ratio of two independent Dagum random variables., Operations Research and Decisions, 20(3&4), 95-102.
- Domma, F., Latorre, G. and Zenga, M. (2012)., The Dagum distribution in reliability analysis., Statistica and Applicazioni., 10(2), 97-113.
- Domma, F., Giordano S. and Zenga, M. (2011)., Maximum likelihood estimation in Dagum distribution from censored samples., Journal of Applied Statistics, 38(12), 2971-2985.
- Domma, F., Giordano S. and Zenga, M. (2013)., The Fisher information matrix on a type II doubly censored sample from a Dagum distribution., Applied Mathematical Sciences, 7, 3715-3729.
- Domma, F. (2004)., Kurtosis diagram for the log-Dagum distribution., Statistica and Applicatzioni, 2, 3-23.
- Zenga, M.(1996)., La curtosi (Kurtosis)., Statistica, 56(1), 87-101.
- Polisicchio, M. and Zenga, M. (1997)., Kurtosis diagram for continuous variables., Metron., 55(3-4), 21-41.
- Domma, F. and Perri, P.F. (2009)., Some developments on the log-Dagum distribution., Statistical Methods and Applications., 18(2), 205-220.
- Ibrahim, E. and Gokarna, A. (2015)., Transmuted Dagum distribution with applications., Chilean Journal of Statistics, 6, 31-45.
- Eugene, N., Lee, C. and Famoye, F. (2002)., Beta-normal Distribution and its Applications., Communications in Statistics - Theory and Methods, 31(4), 497-512.
- Jones, M. C. (2004)., Family of Distributions Arising from Distribution of Order Statistics., Test., 13(1), 1-43.
- Cordeiro, G. M. and Nadarajah, S. (2011)., Closed form Expressions for Moments of a Class of Beta Generalized Distributions., Brazilian Journal of Probability and Statistics., 25(1), 14-33.
- Zea, L. M., Silva, R. B., Bourguignon, M., Santos, A. M. and Cordeiro, G. M. (2012)., The beta exponentiated Pareto distribution with application to bladder cancer susceptibility., International Journal of Statistics and Probability, 1(2), 8-19.
- Lee, E. T., & Wang, J. (2003)., Statistical methods for survival data analysis., Vol. 476. 3rd. Edn., John Wiley and Sons Ltd., New York. USA, 534. ISBN: 9780471458555
- Chen, G. and Balakrishnan, N. (1995)., A general purpose approximate goodness-of-fit test., J. of Quality. Technol., 27(2), 154-161.