Related Experiment Video
Updated: Aug 24, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Explanation of power law behavior of autoregressive conditional duration processes based on the random multiplicative
1Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
Abstract:
Autoregressive conditional duration (ACD) processes, which have the potential to be applied to power law distributions of complex systems found in natural science, life science, and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is verified that the PDF of the ACD(1) has a power law tail with an arbitrary exponent depending on a model parameter. On the basis of theory of the random multiplicative process a relation between the model parameter and the power law exponent is theoretically derived. It is confirmed that the relation is valid from numerical simulations. An application of the ACD(1) to intervals between two successive transactions in a foreign currency market is shown.
Related Concept Videos
Poisson Probability Distribution
The...
Parametric Survival Analysis: Weibull and Exponential Methods
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Properties of DTFT I
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...
Complex Power
Complex power is defined as the multiplication of the voltage and the complex conjugate of the current. The magnitude of this power, known as apparent power, is measured in volt-amperes (VA). Notably, the angle of the complex power equates to the...
Probability Distributions
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Time-Domain Interpretation of PD Control
Consider the example of control of motor torque. Initially, a positive...
