常见分布¶
离散分布¶
伯努利分布¶
\(X \sim B(p)\)
二项分布¶
\(X \sim B(n,p)\)
泊松分布¶
\(X \sim P(\lambda)\)
近似 \(B(n,p) \sim P(np)\)
失效率、危险率¶
\[ \begin{aligned} P(x < X < x + \mathrm dx \mid X > x) &= \frac{P(x < X < x + \mathrm dx , X > x)}{P(X > x)} \\ &= \frac{P(x < X < x + \mathrm dx)}{P(X > x)} \\ &\approx \frac{F'(x)}{1-F(x)} \mathrm dx \end{aligned} \]
令 \(\lambda(t) = \frac{F'(x)}{1-F(x)}\)，则 \(F(x) = 1 - e^{-\int_{0}^x \lambda(t) \mathrm dt}\) 。
连续分布¶
均匀分布¶
\(X\)