The Dagum-Poisson Distribution: Model, Properties and Application


Abstract


A new four parameter distribution called the Dagum-Poisson (DP) distribution is introduced and studied. This distribution is obtained by compounding Dagum and Poisson distributions. The structural properties of the new distribution are discussed, including explicit algebraic formulas for its survival and hazard functions, quantile function, moments, moment generating function, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics and R\'enyi entropy. Method of maximum likelihood is used for estimating the model parameters. A Monte Carlo simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators and width of the confidence interval for each parameter. A real data set is used to illustrate the usefulness, applicability, importance and flexibility of the new distribution.

DOI Code: 10.1285/i20705948v9n1p169

Keywords: Dagum distribution, Dagum Poisson distribution, Poisson distribution, Moments, Maximum Likelihood Estimation.

References


Adamidis K., Dimitrakopoulou, T., and Loukas, S. (2005). On a Generalization of the Exponential-Geometric Distribution, Statistics & Probability Letters, 73, 259-269.

Adamidis K., and Loukas, S. (1998). A Lifetime Distribution with Decreasing Failure Rate, Statistics & Probability Letters, 39, 35- 42.

Andrews, D.F. and Herzberg, A.M. (1985). Data: A Collection of Problems from Many Fields for the Student and Research Worker, New York: Springer Series in Statistics.

Barlow, R.E., Toland, R.H. and Freeman, T. (1984). A Bayesian Analysis of Stress-Rupture Life of kevlar 49/epoxy Spherical Pressure Vessels, In: Proc. Canad. Conf. Appl. Statist.

New York: Marcel Dekker.

Barreto-Souza, W., Silva, R.B., and Cordeiro, G. M (2010). A New Distribution with Decreasing, Increasing and Upside-down Bathtub Failure Rate, Comput. Statist. Data Anal. 54, 935-944.

Barreto-Souza, W., de Morais, A.L., and Cordeiro, G.M. (2011). The Weibull-Geometric Distribution, J. Stat. Comput. Simul. 81, 645-657.

Barreto-Souza, W., and Cribari-Neto, F. (2009). A Generalization of the Exponential-Poisson Distribution, Statistics & Probability Letters, 79, 2493-2500.

Chambers, J.M., Cleveland, W.S., Kleiner, B., and Tukey, P.A. (1983). Graphical Methods for Data Analysis, Belmont, CA: Wadsworth, (1983).

Chahkandi, M., Ganjali, M. (2009). On Some Lifetime Distributions with Decreasing Fail-

ure Rate, Computational Statistics & Data Analysis, 53, 4433-4440.

Chen, G., and Balakrishnan, N. (1995). A General Purpose Approximate Goodness-of-Fit Test, Journal of Quality Technology, Vol. 27, No. 2, 154-161.

Cooray, K. and Ananda, M.M.A. (2008). A Generalization of the Half-Normal Distribution with Applications to Lifetime Data, Communications in Statistics-Theory and Methods,

(9), 1323-1337.

Dagum, C. (1977). A New Model of Personal Income Distribution: Specication and Estimation, Economie Applique'e, 30, 413 - 437.

Dagum, C. (1980). The Generation and Distribution of Income, the Lorenz Curve and the Gini Ratio, Economie Applique'e, 33, 327-367.

Domma, F., and Condino, F. (2013). The Beta-Dagum Distribution: Denition and Properties, Communications in Statistics-Theory and Methods, in press.

Domma, F., Giordano, S., and Zenga, M. (2011). Maximum Likelihood Estimation in Dagum Distribution from Censored Samples, Journal of Applied Statistics V(38)12, 2971-2985.

Domma, F., (2002). L'andamento della Hazard function nel modello di Dagum a tre parametri, Quaderni di Statistica, 4, 103-114 .

Huang, S., and Oluyede, B. O. (2014). Exponentiated Kumaraswamy Dagum Distribution with Applications to Income and Lifetime Data, Journal of Statistical Distributions and

Applications, 1:8, pages 1-20.

Johnson, N.L, Kotz, S., and Balakrishnan, N. (1994). Continuous Univariate Distributions, volume 1, John Wiley & Sons, New York.

Kleiber, C., (2008). A guide to the Dagum distribution. In: Duangkamon,C. (ed.) Modeling Income Distributions and Lorenz Curves Series: Economic Studies in Inequality, Social Exclusion and Well-Being, 5, Springer, New York.

Kleiber, C., and Kotz, S. (2003). Statistical Size Distribution in Economics and Actuarial Sciences, John Wiley & Sons, Inc.

Kus, C., (2007). A new lifetime distribution, Computational Statistics & Data Analysis, 51, 4497-4509.

Lu, W., and Shi, D. (2011). A new compounding life distribution: the Weibull-Poisson distribution, Journal of Applied Statistics, DOI:10.1080/02664763.2011.575126.

Mahmoudi, E., and Sepahdar, A. (2013). Exponentiated Weibull-Poisson Distribution: Model, Properties and Applications, Mathematics and Computers in Simulation, 92, 76-97.

McDonald, B., (1984). Some Generalized Functions for the Size Distribution of Income, Econometrica, 52(3), 647-663.

McDonald, B., and Xu, J., (1995). A Generalization of the Beta Distribution with Application, Journal of Econometrics, 69(2), 133 - 152.

Morais, A.L., and Barreto-Souza, W. (2011). A Compound Class of Weibull and Power Series Distributions, Computational Statistics & Data Analysis, 55, 1410-1425.

Oluyede, B. O., Pararai, M., and Huang, S. (2014). A New Class of Generalized Dagum Distribution with Applications to Income and Lifetime Data, Journal of Statistical and

Econometric Methods, Vol. 3, No. 2, 125-151.

Pararai, M. Warahena-Liyanage, G. and Oluyede, B. O., (2015). Exponentiated Power Lindley-Poisson distribution: Properties and Applications, To Appear in Communications

in Statistics-Theory and Methods.

Tahmasbi, R., and Rezaei, S. (2008). A Two-Parameter Lifetime Distribution with Decreasing Failure Rate, Computational Statistics & Data Analysis, 52, 3889-3901.


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