# On the non-Poissonian repetition pattern of FRB121102

## TL;DR

This paper analyzes the irregular repetition pattern of FRB121102, showing that a Weibull distribution better models burst intervals than Poissonian statistics, with implications for detection strategies.

## Contribution

It introduces a Weibull distribution model for FRB121102 burst intervals, capturing burst clustering and improving understanding of its repetition pattern.

## Key findings

- Burst intervals are better described by Weibull distribution than Poisson.
- Estimated mean repetition rate is approximately 5.7 per day.
- Clustered burst behavior affects detection probabilities and observation planning.

## Abstract

Rhe Fast Radio Burst FRB121102 has been observed to repeat in an irregular fashion. Using published timing data of the observed bursts, we show that Poissonian statistics are not a good description of this random process. As an alternative we suggest to describe the intervals between bursts with a Weibull distribution with a shape parameter smaller than one, which allows for the clustered nature of the bursts. We quantify the amount of clustering using the parameters of the Weibull distribution and discuss the consequences that it has for the detection probabilities of future observations and for the optimization of observing strategies. \new{Allowing for this generalization, we find a mean repetition rate of r=5.7^{+3.0}_{-2.0} per day and index k=0.34^{+0.06}_{-0.05} for a correlation function \xi(t)=(t/t_0)^{k-1}.