INFORMATION CHANGE THE WORLD

International Journal of Mathematical Sciences and Computing(IJMSC)

ISSN: 2310-9025 (Print), ISSN: 2310-9033 (Online)

Published By: MECS Press

IJMSC Vol.4, No.3, Jul. 2018

Bayesian Normal and T-K Approximations for Shape Parameter of Type-I Dagum Distribution

Full Text (PDF, 549KB), PP.13-22


Views:25   Downloads:0

Author(s)

Hummara Sultan, Uzma Jan, S.P.Ahmad

Index Terms

Dagum distribution;Prior Distribution;Bayesian Statistics Normal approximation;T-K approximation

Abstract

Dagum distribution is a statistical distribution used closely for fitting income and wealth distributions. This distribution has wide application in fields like reliability theory survival analysis, actuarial sciences, and meteorological data. In this article, we obtained Bayes estimators for the shape parameter of Dagum distribution using approximation techniques like normal and T-K approximations. Moreover different informative priors have been considered and a simulation study and three real data sets have been considered to study the efficiency of obtained results.

Cite This Paper

Hummara Sultan, Uzma Jan, S.P.Ahmad,"Bayesian Normal and T-K Approximations for Shape Parameter of Type-I Dagum Distribution", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.4, No.3, pp.13-22, 2018.DOI: 10.5815/ijmsc.2018.03.02

Reference

[1]Ahmed, A. Estimation of  for the three parameter Dagum Distribution. J. of Stat: Adv. in Th. and Appl. 2015, 13(2), 167-178.

[2]Alwan, F.M., Baharum, A., Hassan, G.S. Reliability measurement for mixed mode failures of 33/11 kilovolt electric power distribution stations. PLOS ONE. 2013, 8,1–8. 

[3]Bekker, A., Roux, J. & Mostert, P. A generalization of the compound Rayleigh distribution: using a Bayesian method on cancer survival times. Comm. in Stat.-Th. and Meth. 2000, 29(7), 1419-1433.

[4]Benjamin, S.M., Humberto, V.H., Barry, C.A. Use of Dagum Distribution for Modeling Tropospheric Ozone levels. J. Environ. Stat. 2013, 5(5).

[5]Broderick, O.O., Shujiao, H., Mavis,P. A new class of generalized dagum distribution with applications to income and lifetime data. J. Stat. and Eco. Meth. 2014, 3(2) 

[6]Dagum, C. A New Model of Personal Income Distribution: Specification and Estimation. Economie Appliqu′ee; 1977, 30,413–437.

[7]Dagum, C. The Generation and Distribution of Income, The Lorenz Curve and the Gini Ratio. Economie Appliqu′ee. 1980, 33:327–367.

[8]Domma F., Latorre, G., Zenga, M. The Dagum Distribution in Reliability Analysis. Statistica and Applicazioni, 2012, 10(2), 97–113.

[9]Domma, F. L'andamento della hazard function nel modello di Dagum a tre parametri. Quaderni di Statistica, 2002, 4, 1-12.

[10]Domma, F., Giordano S., Zenga, M. The Fisher information matrix on a type II doubly censored sample from a Dagum distribution. Appl. Mathe. Sci.2013,7, 3715–3729.

[11]Domma, F., Perri, P.F. Some developments on the log-Dagum distribution. Stat. Meth. and Appli. 2009, 18,205–220.

[12]Feigl, P. and Zelen, M. Estimation of exponential probabilities with concomitant information. Biometrics. 1965, 21, 826–838.

[13]Khan, M.Z. Dagum, Inverse Dagum and Generalized Dagum Income Size Distributions. Unpublished M.Phil. Thesis, Department of Statistics, The Islamia University of Bahawalpur, Pakistan. 2013.

[14]Kleiber, C. A guide to the Dagum distribution. In: Duangkamon, C. (Eds.), Modeling Income Distributions and Lorenz Curves Series, Springer, New York. 2008, 97–117. 

[15]Kleiber, C., Kotz, S. Statistical Size Distributions in Economics and Actuarial Sciences. New York: Wiley. Meth and Appl. 2003, 18, 205–220.

[16]Monroy, B.S., Huerta, H.V., Arnold, B.C. (2013): Use of the Dagum distribution for modeling tropospheric Ozone levels. J. Envir. Stat. 2013, 5, 1–11.

[17]Naqash, S., Ahmad, S.P., Ahmed, A. Bayesian Analysis of Dagum Distribution. JRSS.2017, 10 (1), 123-136.

[18]Proschan, F. Theoretical explanation of observed decreasing failure rate. Technometrics.1963, 5, 375–383. 

[19]Sultan. H, Ahmad S.P. Bayesian Approximation Techniques of Topp-Leone Distribution. Inter. Jour. Stat. and Maths. 2015, 2(1), 066-070.

[20]Sultan. H, Ahmad S.P. Bayesian Approximations for Shape Parameter of Generalized Power Function Distribution, JRSS. 2015, 10 (1), 149-159.

[21]Sultan. H, Ahmad. S.P. Bayesian Approximations Techniques for Kumaraswamy Distribution, MTM. 2015, 5, 2224-5804.

[22]Sultan. H., Ahmad. S.P. Bayesian Approximation of Generalized Gamma Distribution under Three Loss Function Using Lindley’s Approximation, JAPS. 2015, 10(1), 21-33.

[23]Tahir, M.H., Cordeiro, G.M., Mansoor, M., Zubair, M. Alzaatreh, A. The Weibull-Dagum Distribution: Properties and Applications. Comm. in Statis- Th. and Meth.2016. 

[24]Tierney. L. And Kadane. J. Accurate Approximations for Posterior Moments and Marginal Densities. J. Amer. Statis. Asso. 1986, 81, 82-86.