Statistics/Distributions/Student-t

Student-t Distribution Student’s t density 325px 325px ν > 0 degrees of freedom (real) x ∈ (−∞; +∞) <br/ >where 2F1 is the hypergeometric function 0 for ν > 1, otherwise undefined 0 0 for ν > 2, ∞ for 1 < ν ≤ 2, otherwise undefined 0 for ν > 3, otherwise undefined for ν > 4, ∞ for 2 < ν ≤ 4, otherwise undefined ... undefined for ν > 0 (x): Bessel functionHurst, Simon, The Characteristic Function of the Student-t Distribution, Financial Mathematics Research Report No. FMRR006-95, Statistics Research Report No. SRR044-95 Student t-distribution (or just t-distribution for short) is derived from the chi-square and normal distributions. We divide the standard normally distributed value of one variable over the root of a chi-square value over its r degrees of freedom. Mathematically, this appears as: where and . External links Interactive Student-T Distribution Web Applet (Java)