# Pseudo-exponential distribution and its statistical applications in econophysics

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## Abstract

In generalized measure theory, \(\sigma \)-\(\oplus \)-measure is a generalization of the classical measure defined on a pseudo-addition. In this paper, the class of pseudo-exponential distributions based on a class of \(\sigma \)-\(\oplus \)-measure is introduced. Some examples of this class are investigated. Then by two real data sets obtained from the last three decades of oil, and the last two decades of the daily natural gas spot prices, we show that the pseudo-exponential distribution is better fitted than exponential distribution using the AIC and BIC information criteria.

## Keywords

Pseudo-operations Pseudo-exponential distribution Moment-generating function Numerical computation## Notes

### Acknowledgements

The authors are very grateful to the anonymous reviewers for their suggestions that have led to a revised version of this paper. Hossein Mehri-Dehnavi was supported by Babol Noshirvani University of Technology with Grant program No. BNUT/390012/97. Hamzeh Agahi was supported by Babol Noshirvani University of Technology with Grant program No. BNUT/392100/97.

### Compliance with ethical standards

### Conflicts of interest

The authors declare that they have no conflict of interest.

### Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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