SOME PROPERTIES OF BETA TRANSMUTED DAGUM DISTRIBUTION WITH APPLICATIONS
DOI:
https://doi.org/10.29244/ijsa.v4i2.646Keywords:
beta dagum distribution, dagum distribution, maximum likelihood method, moments, transmuted distributionAbstract
In this paper, we introduce a new family of continuous distributions called the beta transmuted Dagum distribution which extends the beta and transmuted familys. The genesis of the beta distribution and transmuted map is used to develop the so-called beta transmuted Dagum (BTD) distribution. The hazard function, moments, moment generating function, quantiles and stress-strength of the beta transmuted Dagum distribution (BTD) are provided and discussed in detail. The method of maximum likelihood estimation is used for estimating the model parameters. A simulation study is carried out to show the performance of the maximum likelihood estimate of parameters of the new distribution. The usefulness of the new model is illustrated through an application to a real data set.
Downloads
References
Alwan, F. M., Baharum, A., & Hassan, G. S. (2013). Reliability measurement for mixed mode failures of 33/11 kilovolt electric power distribution stations. PloS One, 8(8): 1–8.
Binoti, D. H. B., Binoti, M. L. M. da S., Leite, H. G., Fardin, L., & Oliveira, J. de C. (2012). Probability density functions for description of diameter distribution in thinned stands of Tectona grandis. Cerne, 18(2): 185–196.
Chen, G., & Balakrishnan, N. (1995). A general purpose approximate goodness-of-fit test. Journal of Quality Technology, 27(2): 154–161.
Cordeiro, G. M., & 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.
Costa, M. (2006). The Dagum model of human capital distribution. Statistica, 66(3): 313–324.
Dagum, C. (1980). The generation and distribution of income, the Lorenz curve and the Gini ratio. Economie Appliquée, 33: 327–367.
Dagum, C. (1997). A systematic approach to the generation of income distribution models. Journal of Income Distribution, 6(1): 105–-126.
Dagum, C. (2006). Wealth distribution models: analysis and applications. Statistica, 66(3): 235–268.
Dagum, C. (2008). A new model of personal income distribution: specification and estimation. In Modeling Income Distributions and Lorenz Curves (pp. 3–25). Springer.
Domma, F. (2004). Kurtosis diagram for the Log-Dagum distribution. Statistica Applicazioni, 2: 3–23.
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(6): 1187–1199.
Domma, F., Giordano, S., & Zenga, M. (2011). Maximum likelihood estimation in Dagum distribution with censored samples. Journal of Applied Statistics, 38(12): 2971–2985.
Domma, F., Giordano, S., & Zenga, M. (2013). The Fisher information matrix on a type II doubly censored sample from a Dagum distribution. Appl. Mathe. Sci, 7: 3715–3729.
Domma, F., Latorre, G., & Zenga, M. (2012). The Dagum distribution in reliability analisys. Statistica & Applicazioni, 10(2).
Domma, F., & Perri, P. F. (2009). Some developments on the log-Dagum distribution. Statistical Methods and Applications, 18(2): 205–220.
Elbatal, I., & Aryal, G. (2015). Transmuted Dagum distribution with applications. Chilean Journal of Statistics (ChJS), 6(2).
Eugene, N., Lee, C., & Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics-Theory and Methods, 31(4): 497–512.
Ivana, M. (2011). Distribution of incomes per capita of the Czech households from 2005 to 2008. Journal of Applied Mathematics, 4: 305–310.
Jones, M. C. (2004). Families of distributions arising from distributions of order statistics. Test, 13(1): 1–43.
Kleiber, C., & Kotz, S. (2003). Statistical size distributions in economics and actuarial sciences (Vol. 470). New York (US): John Wiley & Sons.
Lee, E. T., & Wang, J. (2003). Statistical methods for survival data analysis (Vol. 476). New York (US): John Wiley & Sons.
Lukasiewicz, P., Karpio, K., & Orlowski, A. (2012). The models of personal incomes in USA. Acta Physica Polonica A, 121(2B): B82–B85.
Pant, M., & Headrick, T. C. (2013). An L-moment based characterization of the family of Dagum distributions. Journal of Statistical and Econometric Methods, 2: 17–30.
Pérez, C. G., & Alaiz, M. P. (2011). Using the Dagum model to explain changes in personal income distribution. Applied Economics, 43(28): 4377–4386.
Polisicchio, M., & Zenga, M. (1997). Kurtosis diagram for continuous variables. Metron, 55(3): 21–41.
Pollastri, A., & Zambruno, G. (2010). The distribution of the ratio of two independent Dagum random variables. Operations Research and Decisions, 20(3): 95–102.
Shahzad, M. N., & Asghar, Z. (2013). Comparing TL-Moments, L-Moments and conventional moments of dagum distribution by simulated data. Revista Colombiana de EstadÃstica, 36(1): 79–93.
Zea, L. M., Silva, R. B., Bourguignon, M., Santos, A. M., & 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.
Zenga, M. (1996). La curtosi. Statistica, 56(1): 87–102.
