Overview

In statistical modeling, accurately capturing the underlying patterns and extremes in various datasets is crucial in different fields of study. However, classical distributions are limited in their ability to model datasets with high tails and skewed features, which creates the need for flexible models capable of adapting to a wide range of data patterns. This research proposes a new and flexible class of probability distribution known as the Novel Alpha Power Gumbel-X family of distributions. The new family of distributions was developed using the T-X transformation with the link function. The statistical properties of the new family of distributions are derived. Two special models are introduced, using the Exponential and Weibull distributions as baselines: the novel alpha power Gumbel Exponential and the Novel Alpha Gumbel Weibull distributions. The Novel Alpha Power Gumbel exponential distribution is considered in detail, with parameters estimated using the maximum likelihood method via simulation. Furthermore, two real datasets are adapted to demonstrate the flexibility of the Novel Alpha Power Gumbel Exponential distribution, showing a better fit to other distributions.

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