# Sigma Multiplied Gaussian Distribution

• B
• jaydnul
In summary: If you want to find out how a multiplier affects the values, you would need to look up the equation and use it.
jaydnul
Hi!

Say i have two variables that have independent gaussian distributions of probability of being a certain value when i sample them, what is the likely hood that both will land on a 3 sigma value simultaneously? Is there an equation that easily determines that? Also for other combinations like one at 2 sigma and the other at 3 sigma, or what if i have 3 variables instead of two, etc.

Side question, if i had applied a sigma multiplier of 2x, how does that affect the values?

Thanks!

Prob. of a specific value is 0. Rephrase question - use ranges.

jaydnul said:
Hi!

Say i have two variables that have independent gaussian distributions of probability of being a certain value when i sample them, what is the likely hood that both will land on a 3 sigma value simultaneously?
I will assume that you mean within 3 sigma from the mean.
The probability of a result being within 3 sigma is 0.9974. The probability of two independent, identically distributed results being within 3 sigma is 0.9974 * 0.9974 = 0.9948
jaydnul said:
Is there an equation that easily determines that?
The equation for a result being within a certain sigma from the mean is complicated but there are online calculators and tables that you can use. Here is one. It gives you the probability of a result being between 0 and Z, so you would want to double that to include results between -Z and 0. Once you have a probability, ##p##, from the online link and want to use it for ##n## Independent, Identically Distributed (IID) results, the formula is ##(2 p)^n##.
jaydnul said:
Also for other combinations like one at 2 sigma and the other at 3 sigma, or what if i have 3 variables instead of two, etc.
The probability of a result being within 2 sigma is 0.9544. The probability of two independent, identically distributed results being within 2 sigma is 0.9544 * 0.9544 = 0.9109

The probability of three results within 3 sigma is 0.9974 * 0.9974 * 0.9974 = 0.9922
The probability of three results within 2 sigma is 0.9544* 0.9544* 0.9544= 0.8693

jaydnul said:
Side question, if i had applied a sigma multiplier of 2x, how does that affect the values?
It's not clear to me what you mean by a "sigma multiplier". The formula for any number of sigma values is complicated.

## 1. What is a Sigma Multiplied Gaussian Distribution?

A Sigma Multiplied Gaussian Distribution is a type of probability distribution that is used to model continuous random variables. It is characterized by its bell-shaped curve and is often used in statistics and data analysis.

## 2. How is a Sigma Multiplied Gaussian Distribution different from a regular Gaussian Distribution?

A Sigma Multiplied Gaussian Distribution is similar to a regular Gaussian Distribution, but it includes an additional parameter, sigma, which is multiplied by the standard deviation of the distribution. This allows for more flexibility in modeling data with different levels of variability.

## 3. What is the purpose of using a Sigma Multiplied Gaussian Distribution?

The purpose of using a Sigma Multiplied Gaussian Distribution is to accurately model and analyze data that may have varying levels of variability. It is often used in fields such as finance, engineering, and natural sciences to make predictions and draw conclusions from data.

## 4. How is the sigma value determined in a Sigma Multiplied Gaussian Distribution?

The sigma value in a Sigma Multiplied Gaussian Distribution is determined through statistical methods, such as maximum likelihood estimation, which aim to find the most likely value of sigma that fits the data. It can also be manually adjusted to fit the specific needs of the analysis.

## 5. Can a Sigma Multiplied Gaussian Distribution be used for all types of data?

No, a Sigma Multiplied Gaussian Distribution is most suitable for data that follows a normal distribution, meaning it has a symmetrical bell-shaped curve. It may not accurately model data that has a different distribution, such as skewed or bimodal data.

• Set Theory, Logic, Probability, Statistics
Replies
2
Views
466
• Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
12
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
30
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
2
Views
840