There have been significant developments in the period estimation tools and
methods for analysing high energy pulsars in the past few decades. However,
these tools lack well-standardised methods for calculating uncertainties in
period estimation and other recovered parameters for Poisson--dominated data.
Error estimation is important for assigning confidence intervals to the models
we study, but due to their high computational cost, errors in the pulsar
periods were largely ignored in the past. Furthermore, existing literature has
often employed semi-analytical techniques that lack rigorous mathematical
foundations or exhibit a predominant emphasis on the analysis of white noise
and time series data. We present results from our numerical and analytical
study of the error distribution of the recovered parameters of high energy
pulsar data using the Zn2​ method. We comprehensively formalise the measure
of error for the generic pulsar period with much higher reliability than some
common methods. Our error estimation method becomes more reliable and robust
when observing pulsars for few kilo-seconds, especially for typical pulsars
with periods ranging from a few milliseconds to a few seconds. We have verified
our results with observations of the \emph{Crab} pulsar, as well as a large set
of simulated pulsars. Our codes are publicly available for use.Comment: 18 pages, 23 figures, pre-prin