saaagar10 said:Dear Good people,
I needed a help,
Great if u can suggest some references too!
- what will be the distribution of sum of n F distributed random variables?
- what will be the distribution of sum of n non-central F distributed random variables?
Thanks in advance!
The F distribution is a probability distribution that is used to model the ratio of two independent, normally distributed random variables. It is commonly used in statistical tests, such as ANOVA, to compare variances between groups.
The sum of F distributed random variables can be calculated by adding the individual F variables together. If X and Y are two independent F distributed variables with degrees of freedom (df) 1 and 2, respectively, then the sum Z=X+Y will have an F distribution with df 1+2=3.
The mean of the sum of F distributed random variables is equal to the sum of the individual means, while the variance is equal to the sum of the individual variances. In other words, if X and Y are two independent F distributed variables with means μ1 and μ2 and variances σ1^2 and σ2^2, respectively, then the sum Z=X+Y will have a mean of μ1+μ2 and a variance of σ1^2+σ2^2.
Yes, the sum of F distributed random variables can be used to approximate other distributions, such as the Chi-Squared distribution. This is known as the F approximation to the Chi-Squared distribution, and it is used in many statistical tests, including the F-test and the ANOVA test.
The distribution of sum of F distributed random variables has many real-world applications in fields such as economics, engineering, and medicine. For example, it can be used in analyzing financial data, testing the effectiveness of new medical treatments, and studying the effects of different factors on product quality in manufacturing processes.