Analysis-of-variance producers utilize a class of continuous probability distributions called F-distributions, named in honor of Sir Ronald Fisher.Probabilities for a random variable having an F-distribution are equal to areas under a curve called an F-curve. Recall that a t-distribution depends on the number of degrees of freedom,df. An F-distribution also depends on the number of degrees of freedom but has two numbers of degrees of freedom instead of one.

The first number of degrees of freedom for an F-curve is called the degrees of freedom for the numerator and the second the degrees of freedom for the denominator.

For example: df=(10,2) 10: degrees of freedom for the numerator

2: degrees of freedom for the denominator

We can talk about basic properties about F-curves:

Property 1: The total area under an F-curve is equal to 1.

Property 2: An F-curve starts at 0 on the horzontal axis and extends indefinitely to the right,approaching but never touching the horizontal axis as it does so.

Property 3: An F-curve is not symmetric but is skewed to the right.

A statistical measure of the value of a certain portfolio of securities. The portfolio may be for a certain class of security, a certain industry, or may include the most important securities in a given market, among other options.

The value of an index increases when the aggregate value of the underlying securities increases, and decreases when the aggregate value decreases. An index may track stocks, bonds, mutual funds, and any other security or investment vehicle, including other indices. An index’s value may be weighted; for example, securities with higher prices or greater market capitalization may affect the index’s value more than others.

One of the most prominent examples of an index is the Dow Jones Industrial Average, which is weighted for price and tracks 30 stocks important in American markets

The Fisher index (after the American economist Irving Fisher), is calculated as the geometric mean of PP and PL:

Fisher’s index is also known as the “ideal” price index.

However, there is no guarantee with either the Marshall–Edge worth index or the Fisher index that the overstatement and understatement will exactly cancel the other.

While these indices were introduced to provide overall measurement of relative prices, there is ultimately no way of measuring the imperfections of any of these indices (Paasche, Laspeyres, Fisher, or Marshall–Edge worth) against reality.