Comparative Study of the Median Based Unit Rayleigh and its Generalized Form the Generalized Odd Median Based Unit Rayleigh (2503.11700v1)

Abstract: In the present paper, the author discusses the Generalized Odd Median Base Unit Rayleigh (GOMBUR) in relation to the Median Based Unit Rayleigh (MBUR) to evaluate the additive value of the new shape parameter on the estimation process as regards validity indices, goodness of fit statistics, estimated variances of the estimated parameters and their standard errors. This evaluation is conducted on real datasets. Each dataset is analyzed by fitting different competitor distributions in addition to MBUR and GOMBUR distributions. The parameter estimation is achieved by applying Maximum likelihood estimator (MLE) using Nelder Mead optimizer.