In this paper, we introduce the flexible interpretable gamma (FIG) distribution which has been derived by Weibullisation of the body-tail generalised normal distribution. The parameters of the FIG have been verified graphically and mathematically as having interpretable roles in controlling the left-tail, body, and right-tail shape. The generalised gamma (GG) distribution has become a staple model for positive data in statistics due to its interpretable parameters and tractable equations. Although there are many generalised forms of the GG which can provide better fit to data, none of them extend the GG so that the parameters are interpretable. Additionally, we present some mathematical characteristics and prove the identifiability of the FIG parameters. Finally, we apply the FIG model to hand grip strength and insurance loss data to assess its flexibility relative to existing models.

翻译：在本文中，我们提出了一种灵活的、可解释的伽马（FIG）分布，该分布通过对身体尾部广义正态分布进行韦伯化推导得到。通过图形和数学验证，FIG参数在控制左尾、主体和右尾形态方面具有可解释的作用。广义伽马（GG）分布因其参数的可解释性和方程的易处理性，已成为统计学中处理正数数据的基础模型。尽管存在许多能提供更好数据拟合的广义GG形式，但它们都未能扩展GG以保持参数的可解释性。此外，我们给出了FIG的一些数学特性，并证明了其参数的可辨识性。最后，我们将FIG模型应用于手部握力和保险损失数据，以评估其相较于现有模型的灵活性。