Dhistribusi t-student

{{Probability distribution |
  name       =Student’s t|
  type       =density|
  pdf_image  =|
  cdf_image  =|
  parameters = > 0 degrees of freedom (real)|
  support    =x ∈ (−∞; +∞)|
  pdf        =|

  cdf        =<br/
     >where 2F1 is the hypergeometric function|
  mean       =0 for  > 1, otherwise undefined|
  median     =0|
  mode       =0|
  variance   = for  > 2, ∞ for 1 <  ≤ 2, otherwise undefined|
  skewness   =0 for  > 3|
  kurtosis   = for  > 4|
  entropy    =
 ψ: digamma function,
 B: beta function|
|
  mgf        = undefined|
  char       = for  > 0
 (x): Bessel function
}}
Sajeroning probabilitas lan statistika, Distribusi t-student utawa Student’s t-distribution (asring dicekak dadi 't-distribution') iku sawijining distribusi probabilitas lumintu (continuous probability distribution  sing dianggo nalika nganakaké èstrimasi aji rata-rata (mean) saka sawijining populasi sing ukuran sampelé cilik lan standard déviasi ora diweruhi. 

Dhéfinisi
Fungsi dènsiti probabilitas 
Fungsi dhènsitas probabilitas saka distribusi t-Student sing standard ya iku:

ing ngendi  minangka drajad kabébasan lan  minangka  fungsi Gamma. Bisa uga ditulis:

ing ngendi B iku wujud fungsi Beta.

Kanggo  genep,

 

Kanggo  ganjil,

 

Gambar-gambar iki nuduhaké dhènsitas saka t-distribution tumrap aji  sing tansaya mundhak.  Dhistribusi normal dituduhaké kanthi garis biru minangka pembandhing.  Pirsanana yèn t-distribution (garis abang) dadi luwih cedhak marang dhistribusi normal nalika aji  tansaya gedhé.

 Rujukan 

Pranala njaba 
Earliest Known Uses of Some of the Words of Mathematics (S) (Remarks on the history of the term "Student's distribution")''

Dhistribusi lumintu
Dhistribusi normal