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A notes bivariate power law processes: conditional intensity and parameter estimation techniques
Andi Kresna Jaya1, Nurtiti Sunusi1, Erna Tri Herdiani1
1Stochastics Modelling Research Group, Department of Statistics, Faculty of Mathematics and Natural Sciences, Hasanuddin University, Jl. Perintis Kemerdekaan km 10, Kampus Tamalanrea, Makassar, South Sulawesi, 90245, Indonesia.
Methodsx
|July 11, 2026
Summary
This study models two types of events over time using a bivariate point process. Findings reveal observation duration and event timing significantly influence event rate changes.
Area of Science:
- Statistics
- Stochastic Processes
- Time Series Analysis
Background:
- Point process models are crucial for analyzing random event occurrences.
- Bivariate point processes enable simultaneous analysis of dual event types.
- Understanding event intensity patterns is key in various scientific fields.
Purpose of the Study:
- Develop a conditional intensity model for non-homogeneous bivariate point processes.
- Investigate event rate patterns using a time-dependent power law intensity function.
- Analyze the influence of observation duration and event timing on model parameters.
Main Methods:
- Utilized a conditional intensity model for bivariate point processes.
- Employed a time-dependent power law intensity function with two parameters.
- Parameter estimation via maximum likelihood method.
Main Results:
- Observation duration's effect on parameters is non-linear and interacts with event rate changes.
- Increased observed events correlate with higher initial intensity estimates.
- Both observation duration and event timing significantly impact the rate of change in event rates.
Conclusions:
- The developed model provides insights into complex event rate dynamics.
- Parameter estimation is robust, influenced by data characteristics.
- Findings highlight the interplay between observation scale and temporal event patterns.
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