concavity of mills ratio of the gamma distribution is discussed in details.mills ratio, reciprocally convex concave functions, monotone form of l hospital s nbsp
in mathematics, a schur convex function, also known as s convex, isotonic function and order preserving function is a function f r d → r displaystyle nbsp
basic properties and examples. operations that preserve convexity. the conjugate function. quasiconvex functions. log concave and log convex functions.
in mathematics, a real valued function defined on an interval is called convex if the line segment between any two points on the graph of the function lies above nbsp
armengol gasull and frederic utzet a new proof that f is strictly convex, and we give new sharp bounds of f involving rational functions, as a first application we prove that the reciprocal function of mills ratio f is strictly convex nbsp
mar convex, concave, strictly convex, and strongly convex functions. first and second order characterizations of convex functions. optimality nbsp
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