Concept

Student's t-distribution

Summary
In probability and statistics, Student's t-distribution (or simply the t-distribution) t_\nu is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However, t_\nu has heavier tails and the amount of probability mass in the tails is controlled by the parameter \nu. For \nu = 1 the Student's t distribution t_\nu becomes the standard Cauchy distribution, whereas for \nu \rightarrow \infty it becomes the standard normal distribution N(0,1). The Student's t-distribution plays a role in a number of widely used statistical analyses, including Student's t-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. In the form of the location-scale
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