A Modified Monsef Distribution Using Quadratic Rank Transformation Map

A new distribution is proposed using the Quadratic Rank Transmutation Map (QRTM), which introduces skew to an initially symmetric base distribution. The Monsef distribution serves as the baseline. Various statistical properties, including moments, the moment-generating function, and the characteristic function, are derived. The parameters are estimated using the maximum likelihood estimation method, and the method’s performance is validated through mean squared errors and average biases. Additionally, two real datasets are used to demonstrate the flexibility of the proposed distribution.