# A notes bivariate power law processes: conditional intensity and parameter estimation techniques
> Jaya A.K.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_105043496621
Jurnal / Konferensi: Methodsx
Tahun terbit: 2026
DOI: https://doi.org/10.1016/j.mex.2026.104018
ISSN: 22150161
Kuartil SJR: Q1
Citations: 0

## Authors
- Jaya A.K.

## Abstract
The point process model effectively represents the number of random events occurring over time through its intensity function. When events are of two types, a bivariate point process allows simultaneous analysis of each event’s intensity. This study develops a conditional intensity model for a non-homogeneous bivariate point process over time with an event rate approach that follows a certain pattern over time in the form of a time-dependent power law intensity function with two parameters, an initial intensity parameter and a control parameter governing the change in the event rate over time. Parameter estimation is performed using the maximum likelihood method derived from the probability of one event occurring in a very short interval and the non-occurrence at other times. The results of the analysis show that: • The effect of observation duration on model parameters is not linear but depends on its interaction with the pattern of changes in the event rate over time. • The higher the number of events observed, the higher the estimate of the initial intensity of the event. • Both the duration of observation and the timing of events contribute significantly to determining the rate at which the event rate changes over time.

## Keywords
- Bivariate analysis
- Econometrics
- Intensity (physics)
- Estimation
- Mathematics
- Statistical physics
- Power (physics)
- Estimation theory
- Statistics
- Economics
- Physics
- Optics
- Thermodynamics
- Management

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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