In this article, we extensively study a family of distributions using the trigonometric function. We add an extra parameter to the sine transformation family and name it the alpha-sine-G family of distributions. Some important functional forms and properties of the family are provided in a general form. A specific sub-model alpha-sine Weibull of this family is also introduced using the Weibull distribution as a parent distribution and studied deeply. The statistical properties of this new distribution are investigated and intended parameters are estimated using the maximum likelihood, maximum product of spacings, least square, weighted least square, and minimum distance methods. For further justification of these estimates, a simulation experiment is carried out. Two real data sets are analyzed to show the suggested model’s application. The suggested model performed well compares to some existing models considered in the study.

This paper investigates various estimation methods for the parameters of the unit Lindley distribution (U-LD) under both ranked set sampling (RSS) and simple random sampling (SRS) designs. The distribution parameters are estimated using the maximum likelihood estimation, ordinary least squares, weighted least squares, maximum product of spacings, minimum spacing absolute distance, minimum spacing absolute log-distance, minimum spacing square distance, minimum spacing square log-distance, linear-exponential, Anderson–Darling (AD), right-tail AD, left-tail AD, left-tail second-order, Cramér–von Mises, and Kolmogorov–Smirnov. A comprehensive simulation study is conducted to assess the performance of these estimators, ensuring an equal number of measuring units across both designs. Additionally, two real datasets of items failure time and COVID-19 are analyzed to illustrate the practical applicability of the proposed estimation methods. The findings reveal that RSS-based estimators consistently outperform their SRS counterparts in terms of mean squared error, bias, and efficiency across all estimation techniques considered. These results highlight the advantages of using RSS in parameter estimation for the U-LD distribution, making it a preferable choice for improved statistical inference.

In this paper, the ranked set sampling method (RSS) is considered for estimating the inverse power Lindley distribution (IPLD) parameters and compared with the commonly simple random sampling. Different estimation methods are investigated including the commonly maximum likelihood, minimum distance estimation methods (Anderson Darling (AD), right tail Anderson Darling, left tail Anderson Darling, AD left tail second order, Cramér-von Mises), methods of maximum and minimum spacing distance (maximum product spacing distance, minimum spacing distance), methods of ordinary and weighted least squares, and the Kolmogorov–Smirnov method. A simulation study is conducted to compare these methods using RSS and SRS based on the same number of measured units in terms of mean squared error, bias, efficiency, and mean relative estimation error. A failure data set is fitted to the IPLD and the proposed estimation methods are applied to the data.

This study investigates a range of parameter estimation methods for the Half-Logistic Inverse Rayleigh Distribution (HLIRD) under two distinct sampling frameworks: ranked set sampling (RSS) and simple random sampling (SRS). The estimation techniques considered include maximum likelihood estimation, ordinary and weighted least squares, and the maximum and minimum product of spacings methods. Model adequacy is evaluated using five goodness-of-fit criteria: the Anderson–Darling (AD) statistic, its right- and left-tail variants, the second-order left-tail AD statistic, and the Cramér–von Mises statistic. An extensive simulation study is conducted to thoroughly evaluate and compare the performance of the proposed estimators while maintaining a fixed total number of observations across both sampling schemes. The practical relevance of the proposed methods is further illustrated through an application to a real dataset consisting of 69 carbon fiber specimens, with tensile strength measurements (in GPa) recorded at a gauge length of 20 mm. The numerical results demonstrate that estimators based on RSS consistently outperform their SRS counterparts across all considered performance measures, including mean squared error, bias, and mean absolute relative error. Overall, the findings highlight the advantages of employing RSS for parameter estimation of the HLIRD, particularly due to its superior efficiency in small-sample scenarios.