The Singh–Maddala distribution: properties and estimation
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Date
2017-03
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Abstract
The Singh–Maddala distribution is very flexible
and most widely used for modeling the income, wage,
expenditure and wealth distribution of the country. Several
mathematical and statistical properties of this distribution
(such as quantiles, moments, moment generating function,
hazard rate, mean residual lifetime, mean deviation about
mean and median, Bonferroni and Lorenz curves and
various entropies) are derived. We establish relations for
the single and product moments of generalized order
statistics from the Singh–Maddala distribution and then we
use these results to compute the first four moments and
variance of order statistics and record values for sample
different sizes for various values of the shape and scale
parameters. For this distribution, two characterizing results
based on conditional moments of generalized order statis
tics and recurrence relations for single moments are
established. The method of maximum likelihood is adopted
for estimating the unknown parameters. For different
parameters settings and sample sizes, the various simula
tion studies are performed and compared to the perfor
mance of the Singh–Maddala distribution. An application
of the model to a real data set is presented and compared
with the fit attained by some other well-known two and
three parameters distributions.