A new four-parameter lifetime model called the Weibull Fréchet distribution is defined and studied. Various of its structural properties
including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Rényi and δ-entropies
and order statistics are investigated. The new density function can be
expressed as a linear mixture of Fréchet densities. The maximum likelihood method is used to estimate the model parameters. The new
distribution is applied to two real data sets to prove empirically its
flexibility. It can serve as an alternative model to other lifetime distributions in the existing literature for modeling positive real data in
many areas.