Multiplicity distributions for $e^{+}e^{-}$ collisions using Weibull distribution

The two parameters Weibull function is used to describe the charged particle multiplicity distribution in $e^{+}e^{-}$ collisions at the highest available energy measured by TASSO and ALEPH experiments. The Weibull distribution has wide applications in naturally evolving processes based on fragmentation and sequential branching. The Weibull model describes the multiplicity distribution very well, as particle production processes involve QCD parton fragmentation. The effective energy model of particle production was verified using Weibull parameters and the same was used to predict the multiplicity distribution in $e^{+}e^{-}$ collisions at future collider energies.