Background Generating distributions from families is a classification system in the world of probability. Instead of having hundreds of isolated distributions, we groupd them into families based on their shared mathematical properties. This not only organizes our knowledge but also provides powerful tools for analyzing data and building effective statistical models. Methods The extended generalized Rayleigh-Nadarajah Haghighi (EOGRNH) distribution was introduced, and its basic statistical features were thoroughly studied. These features include important functions such as the cumulative function (cdf ), probability density function (pdf ), surviva, l and hazard functions. We obtain statistical features including moments, skewness, ku

Background In general, truncated distributions provide a flexible framework that allows for more realistic and accurate representation of constrained data compared to using non-truncated distributions, making them a fundamental element in modern statistical models and the analysis of constrained data. Methods Right – truncated [0,1] exponential Rayleigh distribution ([0,1]-RTERD) for lifetime is presented in this paper. The new distribution contains two parameters, one of scale and another for the shape. Statistical functions of the (RTERD), such as cumulative functions (CDF), probability density (PDF), survival, and hazard functions, are presented in terms of mathematical construction and graphics. Besides, discuss the mathematica

This study aims to investigate the estimation of the parameters of the inverse exponential Rayleigh distribution using the Maximum Likelihood Estimation (MLE) and Ranked Set Sampling (RSS) methods, on account of their importance in modeling across lifespan and reliability data. The model is used on empirical data representing the fracture stress of carbon fibers for both single and saturated fibers, in order to determine the accuracy of the estimation methods in given applications. In addition, the classical model is expanded to a fuzzy model to focus on inherent uncertainty in real-world applications. This is realized by designing fuzzy numbers using Shih-skewed membership functions, which offer greater flexibility in illustrating

This paper introduces and developed a new lifetime distribution known as inverse exponential Rayleigh distribution (IERD). The new two-scale parameters generalized distribution was studies with its distribution and density functions, besides that the basic properties such as survival, hazard, cumulative hazard, quantile function, skewness, and Kurtosis functions were established and derived. To estimate the model parameters, maximum likelihood, and rank set sampling estimation methods were applied with real-life data.

The main aim of this paper is to introduce a new two-parameter distribution called the inverse exponential Rayleigh distribution (IERD) with the investigated of its statistical properties. We introduce some mathematical complexity of statistical properties such as the moment function, moment generating function, factorial moments generating function, quantity function, skewness, and Kurtosis. We utilize Taylor series expansion to obtain these statistical properties. The process establishes the new distribution relied mainly on the survival functions of both the exponential and Rayleigh distributions. For the application, real data were applied to compare the new distribution with some other distributions using the Akaike information criteri

This paper includes a new life distribution referred to as the alpha power, which has three parameters and is constructed by fitting the two-parameter exponential Weibull distribution to the family of alpha power transformation. The new model named alpha power exponential Weibull distribution (APEWD) with three parameters (α, γ,and β). The basic functions of the distribution, such as the cumulative, probability density, survival, and hazard were presented, in addition to the statistical properties of the APEWD, which were included, as moments, moment generating, skewness, skewness, mode, and median. The parameters were estimated using the Maximum Likelihood Method (MLE). Real data is used to apply criteria such as AIC, BIC, and HQC to co