In this article, we introduce a new flexible discrete family of distributions, which accommodates wide collection of monotone failure rates. A sub-model of geometric distribution or a discrete generalization of the exponential model is proposed as a special case of the derived family. Besides, we point out a comprehensive record of some of its mathematical properties. Two distinct estimation methods for parameters estimation and two different methods for constructing confidence intervals are explored for the proposed distribution. In addition, three extensive Monte Carlo simulations studies are conducted to assess the advantages between estimation methods. Finally, the utility of the new model is embellished by dint of two real datasets.

This paper introduces a new one-parameter distribution derived from the Lindley distribution, called the modified Lindley distribution. Its main feature is to operate a simple trade-off between the exponential and Lindley distributions, offering an interesting alternative to these two well-established distributions. We study the main properties of the proposed distribution, with a special emphasis on its moments, reliability parameter and asymptotic distributions of the extreme order statistics. Then, inferential considerations are explored. We discuss the parameter estimation by the moments and maximum likelihood methods. Three applications reveal that the new model has the ability to fit well practical data sets.

This study introduces a novel reflective–formative hierarchical model specification for the classic push–pull tourist motivation construct, aligning its measurement with the theoretical distinction between intrinsic “push” drives and external “pull” attributes. Unlike the traditional reflective-reflective structuring of tourist motivation we defied the higher order factors (novelty, knowledge and facilities as formative. Using partial least squares structural equation modeling (PLS-SEM) on a purposive sample of 319 international tourists, we empirically validate the reflective–formative (reflective first-order, formative second-order) model. The reflective–formative model showed a superior fit and predictive power: it explained substantially more variance in key outcome constructs (social motives (R² = 53.60) and self-actualization (R² = 23.10)) than the traditional reflective–reflective specification (social motives (R² = 49.30) and self-actualization (R² = 21.70)), which is consistent with best-practice guidelines for theoretically grounded models. In contrast, the incorrectly specified reflective–reflective model showed stronger effects between unrelated constructs, supporting concerns that choosing the wrong type of measurement model can lead to incorrect conclusions. By reconciling the push–pull theory with measurement design, this work’s main contributions are a theoretically justified reflective–formative model for tourist motivation, and evidence of its empirical benefits. These findings highlight a methodological innovation in motivation modeling and underscore that modeling push–pull motives formatively yields more accurate insights for theory and practice.