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.
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.
This study introduces a parametric survival model based on a mixture of two Weibull hazard functions to accommodate bathtub-shaped hazard rates. The proposed formulation provides flexible modeling of lifetime data in applications such as engineering and medical studies. Inference for the model, in the presence of censored observations and covariates, is conducted within a Bayesian framework. Prior distributions for the model parameters are specified using empirical Bayesian methods based on a preliminary data analysis. Posterior summaries of interest are obtained via Markov Chain Monte Carlo (MCMC) simulation methods using the OpenBUGS software to generate samples from the joint posterior distribution of the model parameters. The methodology is illustrated through three real data applications, including two engineering datasets and one medical dataset from oncology.
Logistic regression is widely used for binary outcomes, yet generalized maximum entropy (GME) estimators are often recommended when data are limited or ill-conditioned. Applied guidance on when GME and logistic regression provide practically similar predictive performance—particularly probability calibration—remains limited. We conducted a Monte Carlo study comparing SAS PROC LOGISTIC (maximum likelihood) with SAS PROC ENTROPY (GME-D; GMED) across four baseline scenarios: (S1) large well-specified samples (n = 5000), (S2) small samples with high collinearity (n = 100; corr(x1,x2) ≈ 0.95), (S3) rare events with a quasi-separation tendency (n = 1000; β0 = −3.50; 1% of observations with x1 shifted by +12), and (S4) heavy-tailed contamination/outliers (n = 1000; 5% contaminated with t(1) noise). Each condition was replicated R = 200 times with a 70/30 train–test split. Performance was evaluated on test data using discrimination (AUC), proper scoring rules (Brier score, log loss), and calibration via logistic recalibration (intercept and slope). Across S1–S2, AUC and scoring rules were nearly identical between methods, but PROC ENTROPY produced modestly larger calibration slopes. In S3, AUC remained similar (ΔAUC ≈ 0.0014), while calibration diverged substantially (Δ intercept ≈ 0.456; Δ slope ≈ 0.278). In S4, PROC LOGISTIC showed better discrimination (ΔAUC ≈ −0.0055) and slightly better scoring rules, while PROC ENTROPY again produced larger calibration slopes. Sensitivity analyses varying event prevalence, ESUPPORTS width, and sample size confirmed that calibration differences are most pronounced under rare events and depend on entropy support specifications. Routine calibration reporting is essential when comparing binary classifiers and PROC ENTROPY users should assess sensitivity to ESUPPORTS choices when probability estimation is the goal.
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.
