A New Version of Cubic Rank Transmuted Gumbel Distribution

Abstract

A Cubic Rank Transmuted Gumbel distribution (CTGD) in this article is a new generalization of the Gumbel distribution based on a cubic ranking transmutation map. Examined are the cubic transmuted Gumbel model’s fundamental statistical properties, such as its hazard rate function, moment-generating function, moments, characteristic function, quantile function, entropy, and order statistics. Finally, the usefulness and applicability of the CTGD using two real data sets about waiting time at a bank is described and Wheaton River flood, and the fit has been compared with Gumbel distribution (GD) and transmuted Gumbel distribution (TGD). The results show that the proposed model provides a superior fit than transmuted Gumbel distributions and Gumbel distributions.