Count regression models are important statistical tools to model the discrete dependent variable with known covariates. When the dependent variable exhibits over-dispersion and inflation at zero point, the zero-inflated negative-binomial regression model is used. The presented paper offers a new model as an alternative to the zero-inflated negative-binomial regression model. To do this, Poisson generalized-Lindley distribution is re-parametrized and its parameter estimation problem is discussed via maximum likelihood estimation method. The proposed model is called as zero-inflated Poisson generalized Lindley regression model. The results regarding the efficiency of parameter estimation of the proposed model are evaluated with two simulation studies. To evaluate the success of the proposed model in the case of zero inflation, two datasets are analyzed. According to the results obtained, the proposed model gives better results than the negative-binomial regression model both in case of over-dispersion and in the case of zero inflation.

Statistical models involving bivariate data are among the most important areas of statistical theory. Concomitants of $k$-record values (CKR) are key topics in statistical theory that have not been extensively studied by researchers. In this paper, we derived the marginal distribution of CKR based on the Huang-Kotz Farlie-Gumbel-Morgenstern type Ⅱ (HK–FGM2) family of bivariate distributions. Additionally, we obtained an expression for past extropy associated with the CKR within the HK–FGM2 family. Three related uncertainty measures (the cumulative residual extropy (CREX), cumulative extropy (CEX), and the negative cumulative extropy (NCEX)), were formulated for CKR based on this family. Furthermore, estimation techniques for CREX and NCEX were explored by employing empirical estimators tailored to CKR using the HK–FGM2 family. Finally, we analyzed a computer series system dataset for illustration purposes, providing significant insights into the behavior of CKR uncertainty measures.

The gamma distribution is an essential distribution for modeling data in different areas such as insurance, finance, reliability, and many fields of engineering. This study proposes a new sophisticated distribution as an alternative to the gamma distribution with tractable properties. Mathematical characteristics and the parameter estimation process of the newly defined model are studied. Two datasets from two different disciplines, education and finance, are used to demonstrate the importance of the new model. Moreover, the WMLdist cloud-based application is developed to simplify and spread the use of the proposed distribution.

This paper introduces the Sine New X–Lindley (SNXL) distribution, a new one-parameter lifetime model built by applying a sine transformation to the cumulative distribution function of the New X–Lindley distribution. The model is flexible for positive, skewed data and adds a useful option to reliability and survival analysis. We derived its main properties, including the density, distribution, survival and hazard functions, quantile function, moments, and order statistics, and also studied features such as stochastic ordering and tail behavior. We examined parameter estimation using six methods: maximum likelihood, ordinary least squares, Anderson–Darling, Cramér–von Mises, least squares, and the method of moments. Their performance was compared through a Monte Carlo simulation using bias and mean-squared error. We also extended the model to a fuzzy reliability setting by treating the scale parameter as a fuzzy number and obtaining explicit $\alpha$-cut forms for reliability and mean time to failure. To show its practical value, we applied the SNXL distribution to three real datasets on daily precipitation, heavy precipitation, and household income. In all three cases, it provided the best overall fit among the competing models under the reported goodness-of-fit measures. These results show that the SNXL distribution is a simple and effective model for skewed positive data in reliability, environmental, and economic applications.