Suppose $X_1, \cdots, X_n$ are independent, nonnegative continuous functions, each $X_i$ has hazard function $\lambda_i(x)$.
If $V=\max\{X_1, \cdots, X_n\}$, I need to show that $\lambda_V(x)\leq \min\{\lambda_1(x),\cdots, \lambda_n(x)\}$.
I know that $\displaystyle\lambda_V(x)=\frac{f_V(x)}{1-F_V(x)}=\frac{\sum_j f_j(x)\prod_{i\neq j}F_i(x)}{1-\prod_{i=1}^n F_i(x)}$.
However, I'm stuck here.
Any help would be appreciated.