Distribució t de Student
司徒頓t分布
T-розподіл Стьюдента
T分布
Distribución t de Student
스튜던트 t 분포
Studentsche t-Verteilung
Studentovo rozdělení
Distribuição t de Student
Students t-fördelning
Κατανομή t-Student
Rozkład Studenta
توزيع ستيودنت الاحتمالي
Distribuzione t di Student
Loi de Student
Распределение Стьюдента
Studenten t banaketa
Studentverdeling
Student's t-distribution
T distribution 10df enhanced.svg
T distribution 30df enhanced.svg
T distribution 5df enhanced.svg
T distribution 1df enhanced.svg
T distribution 2df enhanced.svg
T distribution 3df enhanced.svg
center
Density of the distribution for 1, 2, 3, 5, 10, and 30 degrees of freedom compared to the standard normal distribution .
Previous plots shown in green.
where is the modified Bessel function of the second kind
for ,
where is the inverse standardized Student CDF, and is the standardized Student t PDF.
density
Student's
llei de probabilitat
ciągły rozkład prawdopodobieństwa
Wahrscheinlichkeitsverteilung
веројатносна распределба
rozdělení pravděpodobnosti
normalki banatutako populazio baten batezbestekoa lagin txikien bidez estimatzeak sortutako arazoari heltzeko erabiltzen den banaketa estatistikoa
distribución de probabilidade
dewi
loi de probabilité
distribuzione di probabilità continua
sandsynlighedsfordeling
機率分布
probability distribution
December 2020
It is not clear what is meant by "fixed" in this context. An older and more to-the-point source demonstrates that the Student's t distribution with d.o.f. is the maximum entropy solution to a specific problem, for which, in addition to one more constraint, ℰ{ ln} equals some constant which is predetermined for every .
The source does not obviously state this, although it touches upon something related.
Student distribution
undefined
for otherwise undefined
for ∞ for otherwise undefined
where is the hypergeometric function
where : is the digamma function, : is the beta function
degrees of freedom
for for otherwise undefined