Dhistribusi t-student

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Student’s t
Probability density function
Student t pdf.svg
Cumulative distribution function
Student t cdf.svg
Parameters > 0 degrees of freedom (real)
Support x ∈ (−∞; +∞)
PDF
CDF
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
Ex. kurtosis for > 4
Entropy
MGF undefined
CF for > 0

Jroning 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[besut | besut sumber]

Fungsi dènsiti probabilitas[besut | besut sumber]

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 arupa 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.
1df
1 degree of freedom
2df
2 degrees of freedom
3df
3 degrees of freedom
5df
5 degrees of freedom
10df
10 degrees of freedom
30df
30 degrees of freedom

Rujukan[besut | besut sumber]

  1. ^ Hurst, Simon, The Characteristic Function of the Student-t Distribution, Financial Mathematics Research Report No. FMRR006-95, Statistics Research Report No. SRR044-95

Pranala njaba[besut | besut sumber]