Abstract:
Probability distributions are very useful models for characterising inherent variability
in lifetime data.The Weibull distribution is a widely used distribution in
lifetime data analysis and hence has been modified many times to yield new distributions
with greater flexibility. Modified forms of Weibull distribution are widely
used in survival data analysis due to their versatility and relative simplicity. In
this study, a new Odd Kumaraswamy inverse Weibull distribution is developed
and its statistical properties are derived. The model contains several lifetime distributions
as special submodels. The shapes of the probability density function
and the hazard function are discussed. The model parameters are estimated using
maximum likelihood method and a simulation to assess the performance of
maximum likelihood estimators of the parameters is carried out.The average bias
and root mean square error results from the simulation study decrease in terms of
overall trend as the sample size increases indicating asymptotic consistency and
unbiasedness of the estimators. The model is then applied to several survival data
sets namely cancer patients data, guinea pigs data, glass fibres data, and Kelvar
epoxy strand data to illustrate its flexibillity. Applications of the model to survival
data empirically indicate its flexibility and usefulness in modeling various types
of biomedical and reliability data and its superiority over three other lifetime distributions
compared with the model in the study. The model may attract wider
applications in survival analysis, reliability analysis, and insurance.
