A note on some statistical properties of rise time parameters used in muon arrival time measurements

Most investigations of the muon arrival time distribution in EAS during the past decade made use of parameters which can collectively be called rise time parameters. The rise time parameter T sub A/B is defined as the time taken for the integrated pulse from a detector to rise from A% to B% of its full amplitude. The use of these parameters are usually restricted to the determination of the radial dependence thereof. This radial dependence of the rise time parameters are usually taken as a signature of the particle interaction characteristics in the shower. As these parameters have a stochastic nature, it seems reasonable that one should also take notice of this aspect of the rise time parameters. A statistical approach to rise time parameters is presented.