Vol. 6 No. 1 (2023): The Reality of Women in Science

• Innocent Boyle Eraikhuemen
  Department of Physical Sciences, Benson Idahosa University, Benin City, Edo Stat, Nigeria,
  

The Lomax-Exponential distribution has been shown to provide improved flexibility over the classical exponential distribution for modelling lifetime data; however, additional flexibility is often required to adequately capture complex survival patterns encountered in practice. This study proposes a new lifetime distribution called the Alpha Power Transformed Lomax-Exponential Distribution (APTLED) by applying the alpha power transformation to the Lomax-Exponential distribution. The proposed model introduces an additional shape parameter that enhances its ability to model diverse distributional shapes and hazard rate behaviours. Fundamental statistical properties of the distribution, including the probability density function, cumulative distribution function, moments, moment generating function, characteristic function, survival function and hazard rate function, are derived. A simplified form of the probability density function is also developed to facilitate theoretical derivations. The unknown model parameters are estimated using the maximum likelihood estimation method. The practical usefulness of the proposed distribution is demonstrated using remission times of bladder cancer patients and compared with several existing extensions of the exponential and inverse exponential distributions. The performance of the proposed model is evaluated using Akaike Information Criterion (AIC), Consistent Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC), Hannan-Quinn Information Criterion (HQIC), Anderson-Darling, Cramér-von Mises and Kolmogorov-Smirnov goodness-of-fit statistics. Results indicate that the APTLED provides the best overall fit among all competing models, demonstrating its superior flexibility and suitability for modelling positively skewed lifetime data encountered in reliability and survival analysis.

Keywords: Alpha Power Transformation, Lomax-Exponential Distribution, Lifetime Distribution, Maximum Likelihood Estimation, Survival Analysis, Hazard Rate Function, Bladder Cancer Data.