The use of Likert scales in the field of social research is becoming increasingly common; therefore, it is necessary to investigate which is the most appropriate methodology to carry out the analysis of the ordinal data obtained. If they are ordinal, they should be treated as such, however, they are frequently analyzed considering them as continuous variables. One of the most widely used techniques to obtain construct validity evidence based on the internal structure within nomological measurement models is Confirmatory Factor Analysis (CFA). Using simulation studies in which four factors were manipulated (number of factors, number of items response categories, skewness and sample size) our objective is twofold: (1) to examine, under ordinal measurement, the Type I error rate and statistical power associated with common global fit indices, specifically the Root Mean Square Error of Approximation (RMSEA) and the Standardized Root Mean Square Residual (SRMR) when computed under ULS and robust ULS (RULS) estimation; and (2) to evaluate RMSEA and SRMR cut-off values using Receiver Operating Characteristic (ROC) analysis. It is found that, depending on the estimation method chosen, the Type I error and power vary, as well as the values reported by RMSEA and SRMR. RULS seems to obtain better results regardless of experimental factors manipulated. Finally, it is found that it would be convenient to review the cut-off points for these global fit indices recommended by the literature.

In this article, alpha power new logarithmic transformation (APNLT) is proposed to get the new lifetime distributions using some baseline distribution in order to get flexible and superior distributions in terms of fitting to the real data. For the application point of view, we have considered exponential distribution as an appropriate baseline distribution which has constant hazard rate function and thus we have obtained alpha power new logarithmic transformed exponential (APNLTE) distribution. It has increasing, decreasing and upside-down bathtub shapes of failure rate function. Several statistical properties of APNLTE distribution have also been studied. A real dataset is taken to compare this new distribution with some existing distributions.

This study develops a novel bivariate odd Rayleigh-exponential distribution (OR-ED), constructed using the Farlie-Gumbel-Morgenstern (FGM) copula to model dependence between lifetime data. Three estimation methods: maximum likelihood estimation (MLE), inference functions for margins (IFM), and canonical maximum likelihood (CML) are employed to evaluate model performance. Through extensive simulations, all estimators are shown to be consistent, with MLE providing the most accurate estimates and IFM offering a computationally efficient alternative. Practical applications to three real-life datasets demonstrate the flexibility and stability of the proposed model, achieving low biases and RMSEs across the board. The results highlight the model’s suitability for capturing moderate dependence in survival and reliability data, establishing the FGM copula-based OR-ED as an adaptable and efficient tool for joint lifetime analysis.