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"nonnegative_cvar": 0.9995357142857142, "nonnegative_nominal": 0.9998571428571428 }, "0.25": { "q_cvar": 0.024907479766103538, "q_nominal": 0.163793792704129, "coverage_cvar": 0.9011964285714285, "coverage_nominal_cal": 0.8975714285714286, "coverage_uncalibrated": 0.7709464285714287, "nonnegative_cvar": 0.9997321428571428, "nonnegative_nominal": 0.9998571428571428 }, "0.5": { "q_cvar": 0.07175399886604394, "q_nominal": 0.163793792704129, "coverage_cvar": 0.8979642857142857, "coverage_nominal_cal": 0.8975714285714286, "coverage_uncalibrated": 0.275625, "nonnegative_cvar": 0.9998214285714286, "nonnegative_nominal": 0.9998571428571428 }, "1.0": { "q_cvar": 0.16379379270412903, "q_nominal": 0.163793792704129, "coverage_cvar": 0.8975714285714286, "coverage_nominal_cal": 0.8975714285714286, "coverage_uncalibrated": 7.142857142857143e-05, "nonnegative_cvar": 0.9998571428571428, "nonnegative_nominal": 0.9998571428571428 } }, "shifted_test": { "q_cvar": 0.02462645034226122, "q_nominal": 0.1642777720158155, "coverage_cvar": 0.733809523809524, "coverage_nominal_cal": 0.6541904761904763, "coverage_uncalibrated": 0.5544285714285715, "nonnegative_cvar": 0.9037619047619047, "nonnegative_nominal": 0.9216666666666667 }, "predictions": { "exchangeable_coverage": "coverage should be >= 1-alpha in aggregate; finite n gives rank granularity about 1/(n+1)", "alpha_monotonicity": "larger alpha lowers q and target coverage toward 1-alpha", "lower_tail_conservatism": "smaller gamma lowers M_CVaR and should require a smaller/equal residual correction than gamma=1" } }