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Abstract
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Modeling extreme and lifetime data accurately is essential in environmental science, engineering, and medical research. In this study, we propose the Modified Fréchet–Gumbel (MFG) distribution, a flexible model capable of capturing skewness and heavy tails that traditional distributions often fail to represent. We derived its key properties, including the probability density, cumulative distribution, survival, and hazard functions, and estimated parameters using maximum likelihood estimation. Simulation studies are performed to generate random observations from a new modified model .The MFG distribution was evaluated on three real-world datasets: Fort Collins annual maximum precipitation, flood records, and cancer survival times. Its performance was benchmarked against classical models using log-likelihood, AIC, BIC, and the Kolmogorov Smirnov test. Across all datasets, the MFG consistently exhibited superior fit, particularly in capturing extreme observations. These findings demonstrate that the MFG distribution is a powerful and versatile tool for modeling extreme events and survival times. Its flexibility makes it highly suitable for applications in environmental studies, reliability analysis, and biostatistics, providing researchers with a more accurate framework to understand and predict rare but impactful events.
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