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kjetil b halvorsen ♦
kjetil b halvorsen ♦
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I am trying to understand what "overdispersion" means in statistics.

Based on the Wikipedia page, "overdispersion" is defined as follows : "In statistics, overdispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on a given statistical model."

However, I have heard other interpretations of "overdispersion" which suggest that "overdispersion refers to situations where the variance within the data is a function of the mean" - in other words, there is a non-constant relationship between the mean and variance within the data.

My Question: Can someone please tell how to mathematically measure and define "overdispersion"? For instance, I have heard that the Normal Distribution and the Poisson Distribution can be defined as "Dispersion Models". I have also heard that many models can be considered as "Dispersion Models" so long as a "Dispersion Parameter" can be inserted into the model. Using these definitions - is the Normal Distribution an example of "Overdispersion"? For example, there is a lot more variation in a Normal Distribution around the peak - and relatively less variation in a Normal Distribution around the tails. Is all this correct?

Thanks!

References:

I am trying to understand what "overdispersion" means in statistics.

Based on the Wikipedia page, "overdispersion" is defined as follows : "In statistics, overdispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on a given statistical model."

However, I have heard other interpretations of "overdispersion" which suggest that "overdispersion refers to situations where the variance within the data is a function of the mean" - in other words, there is a non-constant relationship between the mean and variance within the data.

My Question: Can someone please tell how to mathematically measure and define "overdispersion"? For instance, I have heard that the Normal Distribution and the Poisson Distribution can be defined as "Dispersion Models". I have also heard that many models can be considered as "Dispersion Models" so long as a "Dispersion Parameter" can be inserted into the model. Using these definitions - is the Normal Distribution an example of "Overdispersion"? For example, there is a lot more variation in a Normal Distribution around the peak - and relatively less variation in a Normal Distribution around the tails. Is all this correct?

Thanks!

References:

I am trying to understand what "overdispersion" means in statistics.

Based on the Wikipedia page, "overdispersion" is defined as follows : "In statistics, overdispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on a given statistical model."

However, I have heard other interpretations of "overdispersion" which suggest that "overdispersion refers to situations where the variance within the data is a function of the mean" - in other words, there is a non-constant relationship between the mean and variance within the data.

My Question: Can someone please tell how to mathematically measure and define "overdispersion"? For instance, I have heard that the Normal Distribution and the Poisson Distribution can be defined as "Dispersion Models". I have also heard that many models can be considered as "Dispersion Models" so long as a "Dispersion Parameter" can be inserted into the model. Using these definitions - is the Normal Distribution an example of "Overdispersion"? For example, there is a lot more variation in a Normal Distribution around the peak - and relatively less variation in a Normal Distribution around the tails. Is all this correct?

References:

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Meaning of "Overdispersion" in Statistics

I am trying to understand what "overdispersion" means in statistics.

Based on the Wikipedia page, "overdispersion" is defined as follows : "In statistics, overdispersion is the presence of greater variability (statistical dispersion) in a data set than would be expected based on a given statistical model."

However, I have heard other interpretations of "overdispersion" which suggest that "overdispersion refers to situations where the variance within the data is a function of the mean" - in other words, there is a non-constant relationship between the mean and variance within the data.

My Question: Can someone please tell how to mathematically measure and define "overdispersion"? For instance, I have heard that the Normal Distribution and the Poisson Distribution can be defined as "Dispersion Models". I have also heard that many models can be considered as "Dispersion Models" so long as a "Dispersion Parameter" can be inserted into the model. Using these definitions - is the Normal Distribution an example of "Overdispersion"? For example, there is a lot more variation in a Normal Distribution around the peak - and relatively less variation in a Normal Distribution around the tails. Is all this correct?

Thanks!

References: