coolamko12 said:derive f distribution as x1 and x2 are independent random variables having a chi-square distribution with n1 and n2 degrees of freedom.. aslo mgf and find raw moments ... and finds its mean and variance.?prove it ?help me guys?
The Snedecor's F distribution is a statistical distribution that is commonly used in hypothesis testing to compare the variances of two populations. It is also used in analysis of variance (ANOVA) to determine if there is a significant difference between the means of multiple groups.
The Snedecor's F distribution is derived by taking the ratio of two independent chi-square distributions divided by their respective degrees of freedom. This ratio follows an F distribution, which is named after the statistician George W. Snedecor.
The main assumption of the Snedecor's F distribution is that the underlying populations from which the samples are taken follow a normal distribution. Additionally, the samples should be independent and the variances should be equal.
In hypothesis testing, the Snedecor's F distribution is used to calculate the F-statistic, which is then compared to a critical value from an F-table. If the calculated F-statistic is greater than the critical value, then it is considered statistically significant and the null hypothesis is rejected.
No, the Snedecor's F distribution is only applicable for parametric data, meaning data that follows a normal distribution. For non-parametric data, other statistical tests such as the Kruskal-Wallis test should be used to compare the variances of multiple groups.