The joint distribution of the maximum and duration of stochastic events driven by Pareto II observations

We study the joint distribution of X and N, where N has the geometric distribution and X is the maximum of the N independent and identically distributed Pareto II (Lomax) observations. The bivariate distribution is referred to as the geometric Marshall-Olkin Lomax distribution (GMOL). A related model for a geometric maximum of IID exponential observations was introduced by Kozubowski and Panorska (2008) and has proven useful in areas such as finance, hydrology and climate. However, the existence of heavy tails in environmental variables motivated this model. Our results for this research include derivations of the joint probability density function, cumulative distribution function, conditional and marginal distributions, conditional survival function, moment-generating function, Laplace transforms, and covariance matrix. We also address the problem of parameter estimation using the method of maximum likelihood. Estimation is empirically verified using a simulation study. We also present results of modeling precipitation and temperature data sets.

Level thesis:degree_level

Master's Degree

Year dc:date.issued

2025

Author dc:creator

• Donkor, Foster

Advisor dc:contributor.advisor

• Panorska, Anna K.

Committee members dc:contributor.committeemember

• Kozubowski, Tomasz J.
• Lu, Minggen
• Kemmelmeier, Markus

• GMOL Model
• Heavy Tail
• Lomax/Pareto Type II Distribution
• Maximum Likelihood Estimation
• Power Law
• Precipitation Data

Language dc:language.iso

en_US, English

Repository record dc:identifier.uri

https://scholarwolf.unr.edu/handle/11714/11556

OAI identifier oai:identifier

oai:scholarwolf.unr.edu:11714/11556