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

Statistical Methods and Data Analysis, Tahtalı,Y. (ed),Bayyurt,L. (ed),Abacı,S. H., Editör, Özgür Publications, Gaziantep, ss.139-164, 2026

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.

Keywords: CRTIW distribution, Lifetime data, Parameter estimation, Monte

Carlo simulation, Statistical modeling