In particular , they derived Chebyshev inequality for distributions with log - concave densities .
developed a general method for deriving the best possible bounds in Chebyshev 's inequality for any family of distributions , and any deviation risk measure in place of standard deviation .
They derived Chebyshev inequality for distributions with log - concave densities .
developed a general method for deriving the best possible bounds in Chebyshev 's inequality for any family of distributions , and any deviation risk measure in place of standard deviation .