import mir.math.common: approxEqual;

assert(3.poissonCCDF(6.0).approxEqual(1.0 - (poissonPMF(0, 6.0) + poissonPMF(1, 6.0) + poissonPMF(2, 6.0) + poissonPMF(3, 6.0))));
// Can compute directly with upper incomplete gamma function
assert(3.poissonCCDF!"gamma"(6.0).approxEqual(poissonCCDF(3, 6.0)));
// For large values of k or lambda, can approximate with normal distribution
assert(1_000_000.poissonCCDF!"approxNormal"(1_000_000.0).approxEqual(poissonCCDF!"gamma"(1_000_000, 1_000_000.0), 10e-3));
// Or closer with continuity correction
assert(1_000_000.poissonCCDF!"approxNormalContinuityCorrection"(1_000_000.0).approxEqual(poissonCCDF!"gamma"(1_000_000, 1_000_000.0), 10e-3));