| Tukey lambda distribution | CDF | ( Q ( p ; λ ) , p ) f o r a n y p : 0 ≤ p ≤ 1 {\displaystyle {\Bigl (}\ Q(p;\lambda ),\ p\ {\Bigr )}~~{\mathsf {for\ any}}~~p\;:\;0\leq \ p\ \leq \ 1~} (general case) 1 e − x +… | 1.00 | infobox |
| Tukey lambda distribution | CF | ϕ ( t ; λ ) = ∫ 0 1 exp ( i t Q ( p ; λ ) ) d p {\displaystyle \phi (t;\lambda )=\int _{0}^{1}\exp {\bigl (}\ i\ t\ Q(p;\lambda )\ {\bigr )}\ \operatorname {d} p~} | 1.00 | infobox |
| Tukey lambda distribution | Entropy | h ( λ ) = ∫ 0 1 ln ( q ( p ; λ ) ) d p {\displaystyle h(\lambda )=\int _{0}^{1}\ln {\bigl (}\ q(p;\lambda )\ {\bigr )}\ \operatorname {d} p~} | 1.00 | infobox |
| Tukey lambda distribution | Excess kurtosis | ( 2 λ + 1 ) 2 ⋅ g 2 2 ⋅ ( 3 g 2 2 − 4 g 1 g 3 + g 4 ) ( 8 λ + 2 ) ⋅ g 4 ⋅ ( g 1 2 − g 2 ) 2 − 3 i f λ > 0 , {\displaystyle ~{\frac {\ (2\ \lambda +1)^{2}\cdot g_{2}^{2}\cdot {\b… | 1.00 | infobox |
| Tukey lambda distribution | Mean | 0 i f λ > − 1 {\displaystyle 0\quad ~{\mathsf {if}}~\quad \lambda >-1\ } | 1.00 | infobox |
| Tukey lambda distribution | Median | 0 | 1.00 | infobox |
| Tukey lambda distribution | Mode | 0 | 1.00 | infobox |
| Tukey lambda distribution | Notation | Tukey(λ) | 1.00 | infobox |
| Tukey lambda distribution | Parameters | λ ∈ ℝ — shape parameter | 1.00 | infobox |
| Tukey lambda distribution | PDF | ( Q ( p ; λ ) , 1 q ( p ; λ ) ) f o r a n y p : 0 ≤ p ≤ 1 {\displaystyle \left(\ Q(\ p\ ;\lambda \ ),\ {\frac {1}{\ q(\ p\ ;\lambda \ )\ }}\ \right)\quad ~{\mathsf {for\ any}}~\… | 1.00 | infobox |
| Tukey lambda distribution | Skewness | 0 i f λ > − 1 3 {\displaystyle 0\qquad \qquad ~{\mathsf {if}}~\quad \lambda >-{\tfrac {\ 1\ }{3}}\ } | 1.00 | infobox |
| Tukey lambda distribution | Support | x ∈ [ −.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-ali… | 1.00 | infobox |
| Tukey lambda distribution | Variance | 2 λ 2 ( 1 1 + 2 λ − Γ ( λ + 1 ) 2 Γ ( 2 λ + 2 ) ) i f λ > − 1 2 {\displaystyle {\frac {2}{\ \lambda ^{2}\ }}\left(\ {\frac {1}{\ 1+2\ \lambda \ }}-{\frac {\ \Gamma \,\!(\lambda… | 1.00 | infobox |
| Tukey lambda distribution | is a | continuous | 0.90 | text |
| Tukey lambda distribution | is a | symmetric distribution | 0.90 | text |
