# Three-parameter generalized exponential distribution in earthquake recurrence interval estimation

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## Abstract

The purpose of this article is to study the three-parameter (scale, shape, and location) generalized exponential (GE) distribution and examine its suitability in probabilistic earthquake recurrence modeling. The GE distribution shares many physical properties of the gamma and Weibull distributions. This distribution, unlike the exponential distribution, overcomes the burden of memoryless property. For shape parameter *β*> 1, the GE distribution offers increasing hazard function, which is in accordance with the elastic rebound theory of earthquake generation. In the present study, we consider a real, complete, and homogeneous earthquake catalog of 20 events with magnitude above 7.0 (Yadav et al. in Pure Appl Geophys 167:1331–1342, 2010) from northeast India and its adjacent regions (20°–32°N and 87°–100°E) to analyze earthquake inter-occurrence time from the GE distribution. We apply the modified maximum likelihood estimation method to estimate model parameters. We then perform a number of goodness-of-fit tests to evaluate the suitability of the GE model to other competitive models, such as the gamma and Weibull models. It is observed that for the present data set, the GE distribution has a better and more economical representation than the gamma and Weibull distributions. Finally, a few conditional probability curves (hazard curves) are presented to demonstrate the significance of the GE distribution in probabilistic assessment of earthquake hazards.

## Keywords

Recurrence interval Memoryless Generalized (exponentiated) exponential distribution Conditional probability Northeast India## Notes

### Acknowledgments

We thank Prof. Debasis Kundu of IIT Kanpur for clarifying many doubts related to the GE distribution. We also thank Dr. R.B.S. Yadav of Kurukshetra University for his suggestions. We are pleased to thank two anonymous reviewers and the editor-in-chief Prof. Thomas Glade for their constructive comments and useful suggestions for improving the present work. Financial support to S.P. by CSIR, India, is duly acknowledged.

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