This paper presents a new probability distribution called the DUS Lindley distribution, created by applying the DUS transformation to the traditional Lindley distribution. The study provides an in-depth analysis of the distribution's statistical properties. These properties include a variety of statistical measures such as the probability density function, cumulative distribution function, failure rate, survival function, reverse hazard function, Mills ratio, mean residual life, mean past life, moments, conditional moments, characteristic function, order statistics, entropy measures, likelihood ratio test and Lorenz and Bonferroni curves. Parameter estimation is performed using several methods including weighted least squares, maximum likelihood estimation, Cramer-Von Mises estimation, least squares and Anderson-Darling estimation. The paper also explores the estimation of system reliability and evaluates the performance of maximum likelihood estimators through simulation studies across different sample sizes. Finally, the DUS Lindley distribution is applied to two real-world datasets, demonstrating a better fit than other well-known distributions.

In this paper, we have proposed a new version of power lindley distribution known as weighted power lindley distribution. The different structural properties of the newly model have been studied. The maximum likelihood estimators of the parameters and the Fishers information matrix have been discussed. It also provides more flexibility to analyze complex real data sets. An application of the model to a real data set is analyzed using the new distribution, which shows that the weighted power Lindley distribution can be used quite effectively in analyzing real lifetime data.

In this research, we establish the novel sin-G class, an innovative and comprehensive class of trigonometric distributions centered on the sine function. A sin-G class analytical approach comprises calculations for the probability density function and reliability indicators. Various estimation methods were presented to estimate the specified model parameters. Applying randomly created datasets and the provided estimating techniques, the behavior of these variables was investigated. Then, the focus is directed toward a specific member of this class, the novel sin-Lomax distribution, which is established with the Lomax distribution serving as the baseline. Exploring the innovative sin-Lomax distribution’s inferential characteristics, the constructed distribution is then fitted to real datasets, demonstrating the actual application of the Sin-G class.

In this paper, we have presented a novel extension of the Erlang-Truncated Exponential distribution (ETE), called Weighted Erland-Truncated Exponential distribution (WETE), and inspected its statistical properties and application to the system reliability. We calculated the parameters estimation and the Fishers information matrix, which are important for estimating various system component reliabilities. To validate the effectiveness of WETE distribution, the performance comparisons were made using real-life data sets from earthquakes, engineering, and medical sciences. The WETE distribution provides a better fit than other existing distributions. In the context of system reliability, the probability of a system or component functioning well is shown. We have used simulations to predict a system’s performance under different conditions. The results show that the maximum likelihood estimator’s performance improves consistency with large sample sizes in the WETE distribution. Finally, we have discussed the application of WETE in reliability optimization problems. The optimal allocation of reliabilities components is determined using the Lagrange multiplier technique. The effectiveness of reliability optimization is evident in improved system performance. This paper also studied the structural properties of WETE, such as the likelihood ratio test, Renyi and Tsallis entropies, order statistics, and Bonferroni and Lorenz curves.

Nadarajah and Haghighi [1] introduced the alternative to the gamma, Weibull and exponentiated exponential distribution with zero mode and allows for increasing, decreasing and constant hazard rates as an extension of exponential distribution. Later Lemonte [2] described the three parameters as exponentiated of the distribution of Nadarajah and Haghighi [1] and given the name as exponentiated Nadarajah–Haghighi (ENH) distribution. Lemonte [2] obtained the rational properties and application of the ENH distribution as moments, entropies, maximum likelihood estimation and stress–strength estimation etc. In this paper, we have obtained the exact expression for single and product moments of order statistics arising from ENH distribution. By using these expressions, we have computed the means of order statistics for \(n=1,...,8\) and for arbitrarily chosen parameter values. Furthermore, the practical application of our findings was well-suited by the linear combination of these order moments as L-moments. Finally, we interpreted the findings and their future work.