The study deals with a new statistical distribution based on the two-parameter chen distribution and its development into a four-parameter distribution by adding the two parameters of the Gompertz-Neutrosophic family, preceded by the development of a Gene distribution model according to the neutrosophic logic, and the new distribution is called the Gompertz-Neutrosophic chen distribution (NGoC). Many basic statistical and mathematical properties of the proposed distribution are presented. The model parameters are estimated using three statistical estimation methods. To determine the efficiency of the NGoC distribution estimation, Monte Carlo simulation is used to determine the bias, squared errors, and root mean square errors. Finally, to determine the efficiency of the proposed distribution, a practical application will be conducted on real neutrosophic data, and a comparison will be made between the NGoC distribution and five other distributions using six statistical measures, where the results showed the flexibility and efficiency of the proposed neutrosophic distribution.

This study introduces and applies a novel statistical model known as the hybrid Weibull inverse Weibull (HWIW) distribution, which combines the characteristics of the Weibull and inverse Weibull distributions to provide a more flexible model for representing real-world data, especially those characterized by asymmetry or extreme values. The basic functions of the distribution were derived, along with other statistical measures such as moments, the quantile function, and entropy were also derived. The distribution parameters were estimated using three distinct approaches, and their performance was evaluated through a Monte Carlo simulation to assess the performance and precision of each estimation technique. The results were used to show the most accurate estimation method for different samples. The proposed model was utilized to test two practical datasets; the findings demonstrated that the HWIW distribution outperformed six competing IW distributions in terms of model selection metrics. These results confirm the efficiency of the HWIW model’s ability to capture the structure of complex datasets and open the way for its use in multiple applications, including medical, industrial, and social fields, with the potential to be expanded to include multidimensional data or integrated with artificial intelligence techniques.

We introduce a new flexible distribution four-parameter which is called [0,1]Truncated Exponentiated Exponential Burr type X distribution ([0,1] TEE-BX). Using binomial series expansion and exponential expansion, the new distribution is expanded by four parameters. We derive moments, moment generating function, quantile function, order statistics and the Rényi entropy. The maximum likelihood estimation method is used to estimate the parameters of the proposed TEE-BX model [0,1]. Finally, using two real-world data sets, the performance of the [0,1] TEE-BX distribution is explored. Based on the certain goodness of fit criteria, we conclude that the [0,1] TEE-BX distribution has a better fit than the other distributions.

The use of statistical distributions to model life phenomena has received a great deal of attention in various sciences. Recent studies have shown the possibility of statistical distributions in data modeling in applied sciences, especially in environmental sciences. Among them is the inverse Weibull distribution, which is one of the most common statistical models that can be used very effectively in modeling data in the health, engineering, and environmental fields, as well as other fields. This study proposes to present a new generalization for the inverse Weibull distribution, where two new parameters are added to the basic distribution according to the Odd Lomax-G family so that the new generalization is more modern and flexible with real-world data. It is called the Odd Lomax Inverse Weibull (LoIW) distribution. The OLIW distribution comes with an expansion of its pdf and CDF functions by using binomial series, exponential, and Logarithm expansions with many statistical properties such as (Rényi entropy, moments, skewness, kurtosis with the moments generating function (mgf), ordered statistics, as well as the Quantile function), and the four distribution parameters are estimated using the maximum likelihood function (MLEs). To ensure the robustness of the proposed model, a practical application is conducted using the R language on two different types of real data and compared with many other statistical models.

This study aims to extend the Odd Lomax Generalized Exponential (OLGE) distribution to include neutrosophic data, which are generalized by uncertainty and ambiguity. It's done formulate a new probabilistic model based on combining Neutrosophic Logic (NL) with Odd Lomax Generalized Exponential to improve the model's flexibility in dealing with data with uncertain and contradictory shapes. The density function and probability distribution of the proposed neutrosophic model are defined, and some mathematical properties are derived as neutrosophic survival, neutrosophic hazard, Incomplete Moments, and Neutrosophic Quantile. In addition, we present new method for parameter estimation using neutrosophic simulation for three techniques (MLE, LSE, WLSE), and compare the model's performance with other model using information criteria and statistical measures. The model is applied to a real neutrosophic data set characterized by uncertainty (the life in 100 hours of 23 batteries), demonstrating its efficiency in analyzing ambiguous data when compared to other neutrosophic distributions.

In this paper, the Burr type X distribution is represented as a mixture with the hybrid Weibull family, called hybrid hybrid Hybrid Weibull Inverse Burr Type X (HWIBX) distribution in order to justify its usefulness in modeling statistical regularities in extreme values recorded in non-stationary streams of media events, the basic new distribution functions are presented in addition to several statistical and mathematical properties of the hybrid distribution as well as estimating the model parameters by three methods, namely maximum likelihood, least squares, and weighted least squares with Conduct Monte Carlo simulations for the three methods. Finally, these results are illustrated through an example of matching the hybrid distribution with data representing the values Bladder cancer and survival times (given in years) of a group comprising 46 patients treated with chemotherapy alone and knowing the results of the improvement of this expansion through comparison with some other distributions using some Statistical metrics.