*Article* **An Alternate Generalized Odd Generalized Exponential Family with Applications to Premium Data**

**Sadaf Khan 1,\*, Oluwafemi Samson Balogun 2,\*, Muhammad Hussain Tahir 1, Waleed Almutiry 3 and Amani Abdullah Alahmadi 4**


**Abstract:** In this article, we use Lehmann alternative-II to extend the odd generalized exponential family. The uniqueness of this family lies in the fact that this transformation has resulted in a multitude of inverted distribution families with important applications in actuarial field. We can characterize the density of the new family as a linear combination of generalised exponential distributions, which is useful for studying some of the family's properties. Among the structural characteristics of this family that are being identified are explicit expressions for numerous types of moments, the quantile function, stress-strength reliability, generating function, Rényi entropy, stochastic ordering, and order statistics. The maximum likelihood methodology is often used to compute the new family's parameters. To confirm that our results are converging with reduced mean square error and biases, we perform a simulation analysis of one of the special model, namely OGE2-Fréchet. Furthermore, its application using two actuarial data sets is achieved, favoring its superiority over other competitive models, especially in risk theory.

**Keywords:** generalized exponential distribution; generalized exponential distribution; OGE-G family; Rényi entropy; order statistic
