T-distribution

We use t-distribution when we need to estimate both the mean and the standard deviation of a distribution. Unlike the standard normal distribution, the t-distributions have a standard deviation larger than one. A t-distribution has a parameter called degrees of freedom. The larger the degrees of freedom in the t-distribution, the more closely it resembles the standard normal distribution.

What does the term degrees of freedom mean?Suppose there is a manager who heads a division with four departments. She need to allocate her budget $10 million across the four departments. In this case, we can say that a manager needs to set the budget for three departments. So degrees of freedom is three.

If the number of degrees of freedom becomes infinite, the t-distribution becomes identical to the z-distribution.