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: