I.J. Mathematical Sciences and Computing, 2018, 3, 13-22 Published Online July 2018 in MECS (http://www.mecs-press.net) DOI: 10.5815/ijmsc.2018.03.02 Available online at http://www.mecs-press.net/ijmsc Bayesian Normal and T-K Approximations for Shape Parameter of Type-I Dagum Distribution Hummara Sultan a , Uzma Jan b , S.P.Ahmad * a,b,* Department of Statistics, University of Kashmir, Srinagar, 190006, India Received: 25 February 2018; Accepted: 15 March 2018; Published: 08 July 2018 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. Index Terms: Dagum distribution, Prior Distribution, Bayesian Statistics Normal approximation, T-K approximation. © 2018 Published by MECS Publisher. Selection and/or peer review under responsibility of the Research Association of Modern Education and Computer Science 1. Introduction Camilo Dagum [6, 7] gave three-parameter type I and four-parameter type II and Type III distributions for fitting income and wealth distributions. However, the Dagum type I distribution has received more attention because the distribution has monotonically decreasing, upside-down bathtub, bathtub and then upside-down bathtub hazard rate for different values of parameters which led several authors to study the distribution in different fields Domma et al. [9, 11], Benjamin et al.[4]. Monroy et al.[16] used it for modeling tropospheric Ozone levels and Alwan et al. [2] worked with the Dagum distribution for assessing the reliability of an electrical system and for describing diameter in teak stands subjected to thinning at different ages. Different properties, characteristics and parameter estimation of Dagum distribution were studied by Kleiber and Kotz [15], Kleiber [14], Domma et al. [8, 10], Khan [13]. Broderick et al. [5] derived a new class of generalized Dagum distribution and studied its applications to income and life time data to illustrate the usefulness of the model. Aala Ahmed [1] proposed the estimates and asymptotic distribution of Dagum distribution. Tahir et al. * Corresponding author. E-mail address: