การแจกแจงปรกติ
| ฟังก์ชันค้ำจุน: | x ∈ R |
|---|---|
| ความเบ้: | 0 |
| Fisher information: | ( 1 / σ 2 0 0 1 / ( 2 σ 4 ) ) {\displaystyle {\begin{pmatrix}1/\sigma ^{2}&0\\0&1/(2\sigma ^{4})\end{pmatrix}}} |
| ตัวแปรเสริม: | μ ∈ R — mean (location) σ2 > 0 — variance (squared scale) |
| มัธยฐาน: | μ |
| เอนโทรปี: | 1 2 ln ( 2 π e σ 2 ) {\displaystyle {\tfrac {1}{2}}\ln(2\pi e\,\sigma ^{2})} |
| ค่าเฉลี่ย: | μ |
| สัญกรณ์: | N ( μ , σ 2 ) {\displaystyle {\mathcal {N}}(\mu ,\,\sigma ^{2})} |
| ความโด่งส่วนเกิน: | 0 |
| ความแปรปรวน: | σ2 |
| cf: | exp { i μ t − 1 2 σ 2 t 2 } {\displaystyle \exp\{i\mu t-{\tfrac {1}{2}}\sigma ^{2}t^{2}\}} |
| cdf: | 1 2 [ 1 + erf ( x − μ 2 σ 2 ) ] {\displaystyle {\frac {1}{2}}{\Big [}1+\operatorname {erf} {\Big (}{\frac {x-\mu }{\sqrt {2\sigma ^{2}}}}{\Big )}{\Big ]}} |
| ฐานนิยม: | μ |
| pdf: | 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 {\displaystyle {\tfrac {1}{\sqrt {2\pi \sigma ^{2}}}}\,e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}}} |
| mgf: | exp { μ t + 1 2 σ 2 t 2 } {\displaystyle \exp\{\mu t+{\tfrac {1}{2}}\sigma ^{2}t^{2}\}} |
