Student's t distribution

Student's t distribution

English

Alternative forms

• Student's t-distribution

Etymology

From the pen-name of Irish statistician William Sealy Gosset, which he used for a 1908 paper in Biometrika, under the pseudonym Student. The distribution was popularised through the work of Ronald Fisher, who referred to it as Student's distribution and used the letter t to represent the test value.

Noun

Student's t distribution (plural Student's t distributions)

1. (statistics) A distribution that arises when the population standard deviation is unknown and has to be estimated from the data.
   • 2009, Francesco Sardanelli, Giovanni Di Leo, Biostatistics for Radiologists: Planning, Performing, and Writing a Radiologic Study, [2008, Biostatistica in Radiologia], Springer, page 59,

     A complete description of the Student's t distribution is beyond the aims of this book.

   • 2011, Rand Wilcox, Modern Statistics for the Social and Behavioral Sciences: A Practical Introduction, Taylor & Francis (CRC Press), page 155,

     In contrast, the 0.95 confidence interval for μ is (577.1,623.4), assuming T does indeed have a Student's t distribution.

   • 2012, Paul D. Kaplan, Frontiers of Modern Asset Allocation, Wiley, page 358,

     Markowitz contends that the weight of the evidence supports a conclusion that the Student's t-distribution is a better model of stock returns than either the normal distribution or the stable Paretian.

   • 2013, Manuel Ammann, Stephan Süss, Asymmetric dependence patterns in financial time series, Alexandra Dias, Mark Salmon, Chris Adcock (editors), Copulae and Multivariate Probability Distributions in Finance, Taylor & Francis (Routledge), page 95,

     To the best of our knowledge, our study is the first empirical implementation of the skewed t-copula to generate meta-skewed Student's t-distributions.

   • 2014, Mohammad Ahsanullah, B.M. Golam Kibria, Mohammad Shakil, Normal and Student's t Distributions and Their Applications, Springer, page 51,

     The graph of the probability density function of the Student's t distribution is a symmetric and bell-shaped curve, differing for different sample sizes.

Usage notes

• Sometimes referred to as Student's t distribution (a noun phrase with Student's used as determiner).
• The isolated letter t is often italicised.

Synonyms

• (statistics): Student's t, t distribution

Coordinate terms

• bell curve
• Poisson distribution

 

Related terms

• Student's t test

Translations

probability distribution

Czech: Studentovo t-rozdělení n Finnish: t-jakauma, Studentin t-jakauma (fi)