Dhistribusi t-student

name       =Student’s t|
  type       =density|
  pdf_image  =325px|
  cdf_image  =325px|
  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 functionHurst, Simon, The Characteristic Function of the Student-t Distribution, Financial Mathematics Research Report No. FMRR006-95, Statistics Research Report No. SRR044-95
}}
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.

+ Density of the t-distribution (red) for 1, 2, 3, 5, 10, and 30 df compared to the standard normal distribution (blue).Previous plots shown in green. thumb|center|240x240px|alt=1df|1 degree of freedom thumb|center|240x240px|alt=2df|2 degrees of freedom thumb|center|240x240px|alt=3df|3 degrees of freedom thumb|center|240x240px|alt=5df|5 degrees of freedom thumb|center|240x240px|alt=10df|10 degrees of freedom thumb|center|240x240px|alt=30df|30 degrees of freedom

 Rujukan 

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

Kategori:Dhistribusi lumintu
Kategori:Dhistribusi normal