The transmuted log-logistic regression model: a new model for time up to first calving of cows

In this paper we introduce a general class of survival regression models, the transmuted log-logistic regression model, which is conceived by a quadratic rank transmutation map applied the usual log-logistic model. We provide a comprehensive description of the properties of the proposed distribution along with a study of its hazard function. Closed expressions for several probabilistic measures are provided, such as probability density function, function hazard, moments, quantile function, mean, variance and median. Inference is maximum likelihood based. Simulation studies are performed in order to evaluate the asymptotic properties of the parameter estimates. The usefulness of the transmuted log-logistic regression distribution for modeling survival data is illustrated on a polled Tabapua breed time up to first calving data.