An entropy measure of uncertainty has a complementary dual function called extropy. In the last six years, this measure of randomness has gotten a lot of attention. It cannot, however, be applied to systems that have survived for some time. As a result, the idea of residual extropy was created. To estimate the extropy and residual extropy, Bayesian and non-Bayesian estimators of unknown parameters of the exponentiated gamma distribution are generated. Bayesian estimators are regarded using balanced loss functions like the balanced squared error, balanced linear exponential and balanced general entropy. We use the Lindley method to get the extropy and residual extropy estimates for the exponentiated gamma distribution based on generalized type-Ⅰ hybrid censored data. To test the effectiveness of the proposed methodologies, a simulation experiment was carried out, and the actual data set was studied for illustrative purposes. In summary, the mean squared error values decrease as the number of failures increases, according to the results obtained. The Bayesian estimates of residual extropy under the balanced linear exponential loss function perform well compared to the other estimates. Alternatively, the Bayesian estimates of the extropy perform well under a balanced general entropy loss function in the majority of situations.

This study provided a significant contribution to developing an adaptable trigonometric extension of the power half-logistic distribution. To be more specific, we created an innovative two-parameter lifetime model called the sine power half-logistic distribution (SPHLD) by using features from the sine-generated family of distributions. The novel distribution could be more effective in modeling lifetime phenomena when asymmetric data was presented, which was the primary motivating factor. The SPHLD's density function plots showed that the distribution adopted several asymmetric shape configurations. Furthermore, the SPHLD's hazard rate plots displayed both monotonic increases and decreases. The quantile function, moments, incomplete moment, and stress-strength reliability were among the statistical characteristics of the SPHLD that were computed. Statistical inference using sixteen distinct classical estimating techniques was utilized to estimate the SPHLD parameters. A simulation study was done to evaluate the consistency of the different estimates and determine the best estimating approach based on some accuracy measures. Analyses of real data revealed that the SPHLD performed better than a number of alternative distributions.

The arctan uniform distribution (AUD) is a brand-new bounded distribution that may be used for modeling a variety of existing bounded real-world datasets. Ranked set sampling (RSS) is a useful technique for parameter estimation when accurate measurement of the observation is challenging and/or expensive. In the current study, the parameter estimator of the AUD is addressed based on RSS and simple random sampling (SRS) techniques. Some of the popular conventional estimating techniques are considered. The efficiency of the produced estimates is compared using a Monte Carlo simulation. It appears that the maximum product spacing method has an advantage in assessing the quality of proposed estimates based on the outcomes of our simulations for both the SRS and RSS datasets. In comparison to estimates produced from the SRS datasets, it can be seen that those from the RSS datasets are more reliable. This implies that RSS is a more effective sampling technique in terms of generating estimates with a smaller mean squared error. The benefit of the RSS design over the SRS design is further supported by real data results.

Entropy measures have been employed in various applications as a helpful indicator of information content. This study considered the estimation of Shannon entropy, $\zeta$-entropy, Arimoto entropy, and Havrda and Charvat entropy measures for the Weibull distribution. The classical and Bayesian estimators for the suggested entropy measures were derived using generalized Type Ⅱ hybrid censoring data. Based on symmetric and asymmetric loss functions, Bayesian estimators of entropy measurements were developed. Asymptotic confidence intervals with the help of the delta method and the highest posterior density intervals of entropy measures were constructed. The effectiveness of the point and interval estimators was evaluated through a Monte Carlo simulation study and an application with actual data sets. Overall, the study's results indicate that with longer termination times, both maximum likelihood and Bayesian entropy estimates were effective. Furthermore, Bayesian entropy estimates using the linear exponential loss function tended to outperform those using other loss functions in the majority of scenarios. In conclusion, the analysis results from real-world examples aligned with the simulated data. Drawing insights from the analysis of glass fiber, we can assert that this research holds practical applications in reliability engineering and financial analysis.