Microergodicity effects on ebullition of methane modelled by Mixed Poisson process with Pareto mixing variable

•A simple Mixed Poisson Process with Pareto mixing is introduced.•We probabilistically model the ebullition of methane emissions from sedge-grass marsh.

We model the process of exceedences of the ebullition of methane from wetlands in the sedge–grass marsh, South Bohemia, Czech Republic by a Mixed Poisson process with mixing variable that is Pareto distributed. We investigate the properties of this process and describe it as a particular case of a counting process. We define Mixed Poisson Pareto random variable, Exponential–Pareto and Erlang–Pareto distributions and investigate their properties.