Transforming a % variation of the mean from Poisson to σ

In summary, the conversation discusses a problem regarding a set of values following a Poisson distribution with a mean value of <m>. The speaker needs to gather another set of data where the mean value is varied by 5%. They are looking for a way to connect these new values to sigma deviations from the original dataset. The other speaker requests for a mathematical explanation using random variables, probabilities, expectations, and variances.
  • #1
Alkass
20
0
Hi!

I do have this problem - Consider that for a set of values, I do have a Poisson distribution with mean value <m> - Now, I need to gather another set of dataset, which I should vary the mean value by 5% - My question is, how can I translate each one of these new values to sigma deviations from the principal dataset , ie how to make a connection between the "varied" value and sigma deviations ?

Thanks

Alex
 
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  • #2
Hey Alkass and welcome to the forums.

Can you show what you mean mathematically (in terms of random variables, probabilities, expectations, and variances)?
 

Related to Transforming a % variation of the mean from Poisson to σ

1. What is a % variation of the mean from Poisson?

The % variation of the mean from Poisson refers to the amount of deviation or difference between the observed mean and the theoretical mean in a Poisson distribution. It is expressed as a percentage and can be used to measure the spread or variability of data in a Poisson distribution.

2. How is a % variation of the mean from Poisson calculated?

To calculate the % variation of the mean from Poisson, you first need to find the theoretical mean of the Poisson distribution. This can be done by taking the average of all the possible values in the distribution. Next, you calculate the observed mean by taking the average of the actual data. Then, you subtract the theoretical mean from the observed mean and divide the result by the theoretical mean. Finally, you multiply the result by 100 to get the % variation.

3. What does it mean to transform a % variation of the mean from Poisson to σ?

Transforming a % variation of the mean from Poisson to σ means converting the % variation into standard deviation (σ). This is done by multiplying the % variation by the theoretical mean and dividing the result by 100. The resulting value is the standard deviation, which is a measure of how much the data deviates from the mean in a Poisson distribution.

4. Why is it important to transform a % variation of the mean from Poisson to σ?

Transforming a % variation of the mean from Poisson to σ is important because it allows us to compare the spread of data in a Poisson distribution to other types of distributions that are measured in standard deviation. This transformation also makes it easier to interpret and analyze the variability of data in a Poisson distribution.

5. Are there any limitations to transforming a % variation of the mean from Poisson to σ?

Yes, there are limitations to transforming a % variation of the mean from Poisson to σ. This transformation assumes that the data follows a Poisson distribution, which may not always be the case. In addition, this transformation does not work well for data with extremely low or high mean values, as it can result in a large standard deviation that may not accurately represent the variability of the data.

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