Determining Overlap of Two Gaussians Mathematically

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In summary, the purpose of determining overlap of two Gaussians mathematically is to quantify the degree to which two normal distributions overlap with each other. This can provide insight into the similarity or difference between two sets of data and can be useful in various statistical analyses. The overlap of two Gaussians is typically calculated by finding the area under the curve of the two distributions that overlap with each other, using integration techniques or statistical software. It provides information about the shared area between the two distributions and can be interpreted as a measure of similarity or dissimilarity depending on the context. However, there are limitations to using this method, such as assuming normal distribution and only considering shared area, which should be taken into account when using it in statistical analyses.
  • #1
fk08
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Hello,

how is the overlap of two gaussians determined mathematically?

Thanks
 
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  • #2
Yes,
it is done by convolution. Details can be seen by goggling convolution.
 
  • #3
fk08 said:
Hello,

how is the overlap of two gaussians determined mathematically?

Thanks

Do you mean the points of intersection of two distributions, or the form of the sum/difference of two distributions, or the amount of probability contained in a region of overlap?
 

1. What is the purpose of determining overlap of two Gaussians mathematically?

The purpose of determining overlap of two Gaussians mathematically is to quantify the degree to which two normal distributions overlap with each other. This can provide insight into the similarity or difference between two sets of data and can be useful in various statistical analyses.

2. How is overlap of two Gaussians calculated?

The overlap of two Gaussians is typically calculated by finding the area under the curve of the two distributions that overlap with each other. This can be done using integration techniques or by using statistical software to calculate the probability of overlap.

3. What information does overlap of two Gaussians provide?

The overlap of two Gaussians provides information about the shared area between two normal distributions. This can be used to determine the similarity or dissimilarity of two sets of data and can also give insight into the probability of certain events occurring within the overlap region.

4. How is overlap of two Gaussians interpreted?

The interpretation of overlap of two Gaussians depends on the context in which it is being used. In general, a higher overlap indicates a greater similarity between the two distributions, while a lower overlap suggests a greater difference. However, the specific interpretation may vary depending on the specific application and the data being analyzed.

5. Are there any limitations to using overlap of two Gaussians to compare data sets?

Yes, there are limitations to using overlap of two Gaussians as a measure of data similarity. This method assumes that the data is normally distributed, which may not always be the case. Additionally, it only considers the shared area between the two distributions and may not take into account other important characteristics of the data. It is important to consider these limitations when using overlap of two Gaussians in statistical analyses.

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