# توزیع مثلثی

پرش به ناوبری پرش به جستجو
پارامترها ${\displaystyle a:~a\in (-\infty ,\infty )}$${\displaystyle b:~b>a\,}$${\displaystyle c:~a\leq c\leq b\,}$ تابع چگالی احتمال تابع توزیع تجمعی ${\displaystyle a\leq x\leq b\!}$ ${\displaystyle \left\{{\begin{matrix}{\frac {2(x-a)}{(b-a)(c-a)}}&\mathrm {for\ } a\leq x\leq c\\&\\{\frac {2(b-x)}{(b-a)(b-c)}}&\mathrm {for\ } c\leq x\leq b\end{matrix}}\right.}$ ${\displaystyle \left\{{\begin{matrix}{\frac {(x-a)^{2}}{(b-a)(c-a)}}&\mathrm {for\ } a\leq x\leq c\\&\\1-{\frac {(b-x)^{2}}{(b-a)(b-c)}}&\mathrm {for\ } c\leq x\leq b\end{matrix}}\right.}$ ${\displaystyle {\frac {a+b+c}{3}}}$ ${\displaystyle \left\{{\begin{matrix}a+{\frac {\sqrt {(b-a)(c-a)}}{\sqrt {2}}}&\mathrm {for\ } c\!\geq \!{\frac {b\!-\!a}{2}}\\&\\b-{\frac {\sqrt {(b-a)(b-c)}}{\sqrt {2}}}&\mathrm {for\ } c\!\leq \!{\frac {b\!-\!a}{2}}\end{matrix}}\right.}$ ${\displaystyle c\,}$ ${\displaystyle {\frac {a^{2}+b^{2}+c^{2}-ab-ac-bc}{18}}}$ ${\displaystyle {\frac {{\sqrt {2}}(a\!+\!b\!-\!2c)(2a\!-\!b\!-\!c)(a\!-\!2b\!+\!c)}{5(a^{2}\!+\!b^{2}\!+\!c^{2}\!-\!ab\!-\!ac\!-\!bc)^{\frac {3}{2}}}}}$ ${\displaystyle -{\frac {3}{5}}}$ ${\displaystyle {\frac {1}{2}}+\ln \left({\frac {b-a}{2}}\right)}$ ${\displaystyle 2{\frac {(b\!-\!c)e^{at}\!-\!(b\!-\!a)e^{ct}\!+\!(c\!-\!a)e^{bt}}{(b-a)(c-a)(b-c)t^{2}}}}$ ${\displaystyle -2{\frac {(b\!-\!c)e^{iat}\!-\!(b\!-\!a)e^{ict}\!+\!(c\!-\!a)e^{ibt}}{(b-a)(c-a)(b-c)t^{2}}}}$