**Definition:** The **F-distribution** depends on the degrees of freedom and is usually defined as the ratio of variances of two populations normally distributed and therefore it is also called as **Variance Ratio Distribution**.

## Properties of F-Distribution

There are several properties of F-distribution which are explained below:

- The F-distribution is
**positively skewed**and with the increase in the degrees of freedom ν_{1}and ν_{2}, its skewness decreases. - The value of the F-distribution is always
**positive, or zero**since the variances are the square of the deviations and hence cannot assume negative values. Its value lies between**0 and****∞**. - The statistic used to calculate the value of mean and variance is:
- The shape of the F-distribution
**depends on its parameters**ν_{1}and ν_{2}degrees of freedom. - The values of the area lying on the left-hand side of the distribution can be found out by taking the reciprocal of F values corresponding to the right-hand side and the degrees of freedom in the numerator and the denominator are interchanged. This is called as
**Reciprocal Property of F-distribution**. Symbolically, it can be represented as:This property is mainly used in the situations when the values of the lower tail F values are to be determined corresponding to the upper tail F values.

Thus, these are the properties of F-distribution that tells how the sample is distributed under study and what statistical inferences can be drawn therefrom.

## Leave a Reply