Sample distribution (2) t distribution

Defining T Distributions

Set x ~ N (0,1), y ~χ2 (n), and X, Y are independent of each other, it is called a random variable

　　　　　　　　　　

T distribution (student distribution) subject to degrees of freedom N

Recorded as T~t (n) with a probability density of

Since TN (x) is even function, its graphics are symmetric about Y. When n tends to infinity, the T distribution is limited to the standard normal distribution N (0,1). In other words, when the T distribution is n~∞, TN (x) approaches the expression of the standard normal distribution. When n is relatively small, the gap between the T distribution and the standard is too large.

Application of T-distribution

The sub-site of the T distribution

For a number α (<0α<1), how to find the number C makes the probability p{t>c}=α? This point C is called the upper α-sub-site of the T-distribution, as Tα (n)

That

It is generally known that the integral value is the lower limit. Finish

The contents of this article are referenced from Internet resources.

Sample distribution (2) t distribution