A new invertible bimodal Weibull model.
Weibull distribution; Return time; Bimodal Weibull.
The Weibull distribution is one of the most used models in statistics and applied areas, as it has a simple expression for the probability density function, survival function, and moments. How ever, the Weibull distribution is not able to fit bimodal data. In this work, we propose a new generalization of the three-parameter Weibull distribution, a new invertible bimodal Weibull model (NIBW), which can be bimodal and its cumulative distribution function and quantile function have a simple and closed form, which makes it very interesting in simulation procedures and for the calculation of risk measures in the applied areas. Several properties of the model were studied and the performance of the maximum likelihood estimates of the parameters was tested using Monte Carlo simulation. Furthermore, using four sets of temperature data, we fitted and compared our model with another bimodal distribution and calculate the return time of this data.