Comparative Inference for the Cubic Rank Transmuted Inverse Weibull Distribution Based on Maximum Likelihood and Least Squares Methods

<jats:p>Identifying flexible statistical distributions that can adequately model real-world data is of fundamental importance in many applied fields. In this study, the inferential properties of the Cubic Rank Transmuted Inverse Weibull (CRTIW) distribution are investigated, and its performance is evaluated through both simulation studies and real data applications.Parameter estimation is carried out using maximum likelihood estimation (mle) and least squares estimation (lse) methods. The finite-sample behavior of the estimators is examined via an extensive Monte Carlo (MC) simulation study under different parameter settings and sample sizes. The estimators are compared in terms of bias and mean squared error (mse), showing that mle performs reliably for moderate and large sample sizes, while lse provides competitive results in capturing the empirical distribution structure.The practical applicability of the CRTIW distribution is illustrated using two real datasets. Model comparison is performed using AIC and BIC criteria, along with goodness-of-fit tests including the Kolmogorov–Smirnov (KS), Anderson–Darling (AD), and Cramér–von Mises (CvM) tests. Although AIC and BIC tend to favor simpler models such as the Transmuted Inverse Weibull (TIW) distribution, goodness-of-fit tests and graphical analyses consistently indicate that the CRTIW distribution provides a more adequate representation of the data.The results demonstrate that the CRTIW distribution offers greater flexibility in modeling complex data structures, particularly in capturing both central tendencies and tail behaviors. Overall, the CRTIW distribution is shown to be a robust and effective alternative for modeling lifetime data, with potential applications in reliability and survival analysis.</jats:p>