What are the potential pitfalls of using the normal approximation when the degrees of freedom are small?

Student's t-distribution is defined as the distribution of the random variable t which is - very loosely - the "best" that we can do not knowing the true ... Aug 28, 2020 ... The t-distribution, also known as Student's t-distribution, is a way of describing data that follow a bell curve when plotted on a graph, ... Generate a multivariate Student-t t variate with degrees of freedom nu, location mu, and scale matrix Sigma; may only be used in transformed data and generated ... Mar 7, 2017 ... The performance of the Kalman filter (KF) can deteriorate in such applications because of the close relation to the Gaussian distribution. Sep 3, 2018 ... The skew normal family is great for modeling skewed gaussian data, and the student t distribution is great for outliers. Feb 2, 2019 ... The normal distribution is a special case of Student's t t t-distribution with the ν \nu ν parameter (i.e., the degree of freedom) set to ... Feb 11, 2010 ... I guess I can't leave comments just yet so this will have to be in the form of an answer: Assuming that the distributions have the same ... Definition. The Student t t -distribution is the distribution of the t t -statistic given by t=¯x−μs√n t = x ¯ − μ s n where ¯x x ¯ is the sample mean, ... A standard multivariate Student's t random vector can be written as a multivariate normal vector whose covariance matrix is scaled by the reciprocal of a Gamma ... 1.00. 0.50. 0.40. 0.30. 0.20. 0.10. 0.05. 0.02. 0.01. 0.002. 0.001 df. 1. 0.000. 1.000. 1.376. 1.963. 3.078. 6.314. 12.71. 31.82. 63.66. 318.31. 636.62.