Exponentiated Weibull Distribution for Modeling the Vehicle Headway Data based on Ranked Set Sampling

Modeling the vehicle headway data is fundamental for intelligent transportation applications in traffic engineering. It is useful for the traffic signal optimization and flow modelling. Exponentiated Weibull (EW) is one of the best flexible model for characterizing uncertainty in various fields of data. In this study, we revisit EW distribution and propose to use of ranked set sampling as a useful sampling method for estimating the unknown parameters. We deal with the performance of ranked set sampling and simple random sampling methods by a simulation study in R-software in terms of mean squared errors. We estimate the parameters of EW distribution using the maximum likelihood method under the assumption that all parameters are unknown. We illustrate the flexibility and the usefulness of EW distribution by analysing generated data from a real application study in transportation field.