The probability density function of T distribution is used to estimate the population with normal distribution and unknown variance according to the mean of small samples.

Data expansion:

In probability theory and statistics, T-distribution is used to estimate the mean of a population with normal distribution and unknown variance according to small samples. If the population variance is known (for example, when the number of samples is large enough), normal distribution should be used to estimate the population mean.

The shape of the t distribution curve is related to the size of n (to be exact, the degree of freedom df). Compared with the standard normal distribution curve, the smaller the degree of freedom df, the flatter the T distribution curve, the lower the middle part of the curve and the higher the tails on both sides of the curve. The greater the degree of freedom df, the closer the T distribution curve is to the normal distribution curve. When the degree of freedom df=∞, the T distribution curve is a standard normal distribution curve.

History:

In probability theory and statistics, students' T distribution (students'? T-distribution) is usually used to estimate the average value of the normal distribution population. The significant difference between the two samples is the basis of students' t-test. T-test improves Z-test (en:Z-test), which can be applied regardless of the number of samples.

When the number of samples is large (more than 30), Z- test can be applied, but when Z- test is used for small samples, it will produce great errors, so when the number of samples is small, student T- test should be used instead. When there are more than three groups of data, because the error can not be suppressed, the analysis of variance can be used instead of student t-test. When the standard deviation of the population is unknown but needs to be estimated, the student T distribution can be used.

T-distribution of students can be called T-distribution for short. Its derivation was first published by William Goss in 1908, when he was still working in Guinness Brewery in Dublin. Because it can't be published in its own name, the paper uses the pseudonym of student. Later, through ronald fisher's work, T-test and related theories were developed, and it was he who called this distribution student distribution.