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The quest by researchers in the area of distribution theory in proposing new models with greater flexibility has filled literature. On this note, we proposed a new distribution called the new extended generalized inverse exponential distribution with five positive parameters, which extends and generalizes the extended generalized inverse exponentia...
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... data was used by Yousof et al. [18]. The data are: 0. 39, 0.85, 1.08, 1.25, 1.47, 1.57, 1.61, 1.61, 1.69, 1.80, 1.84, 1 3.09, 3.11, 3.11, 3.15, 3.15, 3.19, 3.22, 3.22, 3.27, 3.28, 3.31, 3.31, 3.33, 3.39, 3.39, 3.56, 3.60, 3.65, 3.68, 3.70, 3.75, 4.20, 4.38, 4.42, 4.70, 4.90. Table 1 shows the result of the analysis of data set representing the breaking stress of carbon fibers of 50 mm length (GPa). ...
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... The pdf of the order statistics for the TLEGoIRa distribution is obtained as follows: [21][22][23][24] ( ) ( ) ( ) ( ) ...
This paper focused on deriving a new lifetime distribution having five parameters by compounding the Gompertz inverse Rayleigh model and the Topp-Leone exponentiated-G family of distributions. The new model is called Topp-Leone exponentiated Gompertz inverse Rayleigh (TLEGoIRa) distribution. The new model is very flexible and the shape of its pdf can be positively or negatively skewed and symmetric. Some statistical characteristics of the new model, such as the moments, incomplete moments, quantile function, rényi entropy and order statistics are derived and investigated. The pdf of the minimum and maximum order statistics of the new model were derived and studied. The model's parameters are estimated using the maximum likelihood approach. A simulation study was conducted to investigate the consistency of the newly proposed model, using the average bias and root mean square error (RMSE) as metrics. The outcome of the simulation suggested that as sample sizes increase, both the average bias and root mean square error (RMSE) decrease, indicating that the distribution is consistent. Finally, two real-life datasets were used to explore the new model's importance and adaptability in comparison to other competing models The results of the application revealed that the new distribution outperforms its competitors.
... This skewness poses a significant challenge to conventional distributions, prompting researchers to explore extensions of established models to better capture these complexities. Notable among these extensions are the works of [1] - [9]. In this study, we focus on extending the Gompertz inverse Rayleigh (GoIR) distribution, introduced by [10], to create a more adaptable model. ...
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