|
Abstract
|
In this article,we define a new lifetime model called theWeibull–Dagum
distribution. The proposed model is based on the Weibull–G class. It
can also be defined by a simple transformation of the Weibull random
variable. Its density function is very flexible and can be symmetrical,
left-skewed, right-skewed, and reversed-J shaped. It has constant,
increasing, decreasing, upside-down bathtub, bathtub, and reversed-J
shaped hazard rate. Various structural properties are derived including
explicit expressions for the quantile function, ordinary and incomplete
moments, and probability weighted moments. We also provide explicit
expressions for the Rényi and q-entropies. We derive the density
function of the order statistics as a mixture of Dagum densities. We use
maximum likelihood to estimate the model parameters and illustrate
the potentiality of the new model by means of a simulation study and
two applications to real data. In fact, the proposed model outperforms
the beta-Dagum, McDonald–Dagum, and Dagum models in these
applications.
|