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.

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 demonstrates the construction of a modern generalized Exponential Rayleigh distribution by merging two distributions with a single parameter. The "New generalized Exponential-Rayleigh distribution" specifies joining the Reliability function of exponential pdf with the Reliability function of Rayleigh pdf, and then adding a shape parameter for this distribution. Finally, the mathematical and statistical characteristics of such a distribution are accomplished

     This paper discusses estimating the two scale parameters of Exponential-Rayleigh distribution for singly type one censored data which is one of the most important Rights censored data, using the maximum likelihood estimation method (MLEM) which is one of the most popular and widely used classic methods, based on an iterative procedure such as the Newton-Raphson to find estimated values for these two scale parameters by using real data for COVID-19 was taken from the Iraqi Ministry of Health and Environment, AL-Karkh General Hospital. The duration of the study was in the interval 4/5/2020 until 31/8/2020 equivalent to 120 days, where the number of patients who entered the (study) hospital with sample size is (n=785). The number o

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

Methods of estimating statistical distribution have attracted many researchers when it comes to fitting a specific distribution to data. However, when the data belong to more than one component, a popular distribution cannot be fitted to such data. To tackle this issue, mixture models are fitted by choosing the correct number of components that represent the data. This can be obvious in lifetime processes that are involved in a wide range of engineering applications as well as biological systems. In this paper, we introduce an application of estimating a finite mixture of Inverse Rayleigh distribution by the use of the Bayesian framework when considering the model as Markov chain Monte Carlo (MCMC). We employed the Gibbs sampler and

The two parameters of Exponential-Rayleigh distribution were estimated using the maximum likelihood estimation method (MLE) for progressively censoring data. To find estimated values for these two scale parameters using real data for COVID-19 which was taken from the Iraqi Ministry of Health and Environment, AL-Karkh General Hospital. Then the Chi-square test was utilized to determine if the sample (data) corresponded with the Exponential-Rayleigh distribution (ER). Employing the nonlinear membership function (s-function) to find fuzzy numbers for these parameters estimators. Then utilizing the ranking function transforms the fuzzy numbers into crisp numbers. Finally, using mean square error (MSE) to compare the outcomes of the survival