The Complementary Exponentiated Lomax-Poisson Distribution with Applications to Bladder Cancer and Failure Data
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Date
2021-07
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Abstract
A new continuous four-parameter lifetime distribution is introduced by compounding
the distribution of the maximum of a sequence of an independently identically expo
nentiated Lomax distributed random variables and zero truncated Poisson random vari
able, de ned as the complementary exponentiated Lomax Poisson (CELP) distribution.
The new distribution which exhibits decreasing and upside down bathtub shaped density
while the distribution has the ability to model lifetime data with decreasing, increasing
and upside-down bathtub shaped failure rates. The new distribution has a number of
well-known lifetime special sub-models, such as Lomax-zero truncated Poisson distribu
tion, exponentiated Pareto-zero truncated Poisson distribution and Pareto- zero truncated
Poisson distribution. A comprehensive account of the mathematical and statistical prop
erties of the new distribution is presented. The model parameters are obtained by the
methods of maximum likelihood, least squares, weighted least squares, percentiles, max
imum product of spacing and Cramer-von-Mises and compared them using Monte Carlo
simulation study. We illustrate the performance of the proposed distribution by means of
two real data sets and both the data sets show the new distribution is more appropriate
as compared to the transmuted Lomax, beta exponentiated Lomax, McDonald Lomax,
Kumaraswamy Lomax, Weibull Lomax, Burr X Lomax and Lomax distributions.