离散均匀(随机)分布¶
带参数的离散均匀分布 \(\left(a,b\right)\) 构造一个随机变量，该变量成为半开范围内的任意一个整数的概率相等 \([a,b)\) 。如果 \(a\) 则假定它为零，并且唯一的参数是 \(b\) 。所以呢，
\BEGIN{eqnarray*}
p\Left(k，a，b\right)&=&\frac{1}{b-a}\quad a\leq k<b\\
F\Left(x；a，b\Right)&=&\frac{\Left\lFloor x\Right\rFloor-a}{b-a}\quad a\leq x\leq b\\
g\Left(q；a，b\right)&=&\Left\lceil q\Left(b-a\right)+a\right\rceil\\
\m&=&\frac{b+a-1}{2}\\
\MU_{2}&=&\frac{\left(b-a-1\right)\left(b-a+1\right)}{12}\\
\Gamma_{1}&=&0\\
\Gamma_{2}&=&-\frac{6}{5}\frac{\left(b-a\right)^{2}+1}{\left(b-a-1\right)\left(b-a+1\right)}.
\end{eqnarray*}
\BEGIN{eqnarray*}
m\Left(t\Right)&=&\frac{1}{b-a}\sum_{k=a}^{b-1}e^{tk}\\
&=&\frac{e^{bt}-e^{at}}{\left(b-a\right)\left(e^{t}-1\right)}
\end{eqnarray*}