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.