The Student's t-distribution is a statistical model used to approximate the first-order moment of a population with a normal distribution when the sample size it is small and the standard deviation is unknown.
The Student's t distribution estimates the value of a small sample mean that is drawn from a population with a normal distribution, whose standard deviation is unknown.
Given a continuous variable L approximates a t distribution with g degrees of freedom, it is as follows:
L ~ t (g)
The random variable L follows a t distribution with "g" degrees of freedom.
Representation and importance of the Student's t distribution
Source: Thorin, Wikipedia.
Student's t distribution resembles a normal, except that the latter has the followingwider tails than Student's t. Also, for this distribution to grow, more degrees of freedom have to be added, in order to resemble a normal distribution.
The essential importance is that the distribution does not depend on the mean and variance as happens in the normal distribution, but on the degrees of freedom of the Student's t distribution. If we know the degrees of freedom, we can control the distribution.
¿Cuándo se utiliza una distribución t de Student?
It is used when:
- The sample size is less than 30 items (n <30). If they exceed 30 elements, the distribution will follow a normal, so we will use the normal distribution.
- We want to know what is the mean of a population that is distributed according to a normal, through a small sample.
- If we do not know the typical (or standard) deviation of a population and we have to estimate it according to the observations of the sample.