Continuous-time processes with attraction?

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In summary, the conversation is about finding a good model for a population and the potential of using a negative binomial distribution with parameters that can adjust the degree of attraction or repulsion. The speaker also mentions their lack of expertise in statistics and their interest in trying the suggested approach.
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CRGreathouse
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I'm trying to find a good model, and I wanted to find a process that fits. The Poisson process almost fits, but unfortunately the independence assumption is too strong for my data. Is there a similar process that has a parameter (or several) that allow for points to attract or repel others, like zeta zeros?

I've never been good with statistics, so there could be a very simple process I've overlooked, I don't know.
 
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CRGreathouse said:
I'm trying to find a good model, and I wanted to find a process that fits. The Poisson process almost fits, but unfortunately the independence assumption is too strong for my data. Is there a similar process that has a parameter (or several) that allow for points to attract or repel others, like zeta zeros?

I've never been good with statistics, so there could be a very simple process I've overlooked, I don't know.

Negative binomial distribution?
The distribution is described by 2 parameters.
One could be considered a "dispersion" parameter;
a degree of "clumping" in the population?
Maybe it could provide a knob for dialing up or down the degree of attraction or repulsion.
 
  • #3
fopc said:
Negative binomial distribution?
The distribution is described by 2 parameters.
One could be considered a "dispersion" parameter;
a degree of "clumping" in the population?
Maybe it could provide a knob for dialing up or down the degree of attraction or repulsion.

Oh, cool. This looks good -- I'll have to try it with my population to see how well it can model it.

Thanks!
 

FAQ: Continuous-time processes with attraction?

What are continuous-time processes with attraction?

Continuous-time processes with attraction refer to mathematical models that describe the behavior of systems that have a tendency to move towards a certain point or state over time. These processes are commonly used in fields such as physics, chemistry, biology, and economics to study the dynamics of various systems.

How are continuous-time processes with attraction different from other types of processes?

Continuous-time processes with attraction are different from other types of processes, such as random processes, in that they exhibit a consistent and predictable pattern of movement towards a specific point or state. This is in contrast to random processes, which have no predictable pattern and are subject to random fluctuations.

What are some real-world examples of continuous-time processes with attraction?

Continuous-time processes with attraction can be observed in many natural and man-made systems. For example, the motion of a pendulum, the growth of a population, and the spread of a virus can all be modeled as continuous-time processes with attraction. In economics, the movement of prices towards an equilibrium point is also an example of this type of process.

How are continuous-time processes with attraction modeled and analyzed?

Continuous-time processes with attraction are typically modeled using differential equations, which describe how the system changes over time. These equations can then be solved using various mathematical techniques to analyze the behavior of the system and make predictions about its future state.

What are the practical applications of studying continuous-time processes with attraction?

The study of continuous-time processes with attraction has many practical applications in various fields. For example, it can help scientists and engineers understand and predict the behavior of complex systems, design more efficient processes, and make informed decisions in areas such as finance and economics. It also has applications in control theory, where it is used to design controllers for systems that exhibit attraction towards a certain state.

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