This paper introduces a new parsimonious transformation within the T-X family of distributions that generates flexible models without introducing additional parameters. The proposed generator enhances classical distributions by embedding a structurally adaptive mechanism capable of modeling diverse hazard rate shapes—including increasing, decreasing, and bathtub forms—while maintaining computational simplicity. Analytical properties such as linear representation, moments, order statistics, and information-theoretic measures are systematically derived and examined. Maximum likelihood estimation procedures are developed, and a Monte Carlo simulation study evaluates estimator performance under varying sample sizes and parameter settings through bias, mean squared error, and coverage probability. Two submodels—the New Parsimonious Exponential (NPEx) and New Parsimonious Weibull (NPW) distributions—are explored in detail. Their flexibility is demonstrated through visualization, parameter sensitivity analysis, and empirical validation using three real-world datasets: COVID-19 case counts from Kerala (India), flood peak exceedances from the Wheaton River (Canada), and leukemia patient survival times. Model comparison using goodness-of-fit criteria (AIC, BIC,
CAIC, HQIC) and the Nikulin–Rao–Robson statistic confirms that the proposed family achieves superior fit with minimal parameterization, providing a unified and robust framework for lifetime and reliability modeling.

KEYWORDS: T–X family of distributions; Parameter-preserving transformation; Survival analysis; Hydrological modeling; Kerala COVID-19 data; N.R.R statistic.

In this article, we consider a generalized cubic transmuted distribution termed the Exponentiated Cubic Transmuted Uniform Distribution (ECTUD). We studied the mathematical properties as well as the reliability behaviour of the proposed distribution. The maximum likelihood estimation (MLE) method is used for the estimation of parameters. A simulation study is carried out to study the performance of the maximum likelihood estimates of the parameters. The practical applicability of the proposed distribution is illustrated using a real-world dataset.

KEYWORDS:exponentiated cubic transmuted distribution; moments; reliability analysis; order statistics; entropy; simulation.

In this paper, an intervened version of the generalized Gegenbauer distribution is considered and studied some of its statistical properties. The parameters of the distribution are estimated by using the method of maximum likelihood, method of mixed moments and illustrated using real life data sets. The likelihood ratio test procedure is applied for examining the significance of the intervention parameters and a simulation study is carried out for assessing the performance of the estimators.

KEYWORDS: Generalized Gegenbauer distribution, generalized Gegenbauer polynomials, intervened negative binomial distribution, maximum likelihood estimation, probability generating function.

This study introduces a two-parameter generalization of the geometric distribution and investigates its fundamental statistical properties. Closed-form expressions for the probability generating function, cumulative distribution function, mean, variance, mode, index of dispersion, survival function, and hazard rate function are derived. The problem of parameter estimation is addressed using the method of maximum likelihood, and a generalized likelihood ratio test is developed to examine the significance of the additional parameter. The practical usefulness of the proposed distribution is illustrated through applications to real medical data sets. Furthermore, a Monte Carlo simulation study is carried out to assess the finite-sample performance of the estimators. The results demonstrate that the proposed model provides greater flexibility and improved data fitting compared to some existing count data models.

KEYWORDS: count data modeling; probability generating function; maximum likelihood estimation; geometric distribution; survival function; simulation.