On the Odd Kumaraswamy Inverse Weibull Distribution with Application to Survival Data

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.