Generalised M-Transformation Weibull Distribution: Statistical Properties and Reliability Applications

Francis Kwame Arpoh, Gabriel Asare Okyere, Isaac Akpor Adjei

Abstract


Many real-world datasets show complex features that classical life-time models cannot capture. This limitation highlights the need for new distributions with greater flexibility in skewness and kurtosis, as well as improved fit to observed data. In this study, we introduce the Generalised M-Transformation Weibull (GMTW) distribution to meet these needs. We derive its main statistical properties, including the quantile function and reliability measures. The GMTW distribution can represents diverse hazard rate shapes including bathtub, unimodal, and monotonic forms, making it suitable for reliability studies. Parameters are estimated using the maximum likelihood method, and the long run behaviour of the estimators is checked through extensive Monte Carlo simulations. The model’s usefulness is shown with three datasets: industrial reliability, glass fibre tensile strength, and bladder cancer remission times. Likelihood Ratio Tests and goodness-of-fit criteria confirm that the GMTW distribution performs better than its related forms and other well-known lifetime distributions.


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DOI: http://dx.doi.org/10.23755/rm.v56i0.1759

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.