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Retain the same loss distribution
Use the loss law L=μL+σL Z and the confidence quantile zc=Φ⁻¹(c). The normal law has no probability atom at its threshold, so the upper conditional tail has mass 1−c.
Apply the tail-mean multiplier
φ is standard normal density; its height alone is not the tail probability.
Calculate the original case
At 95%, μL=0 and σL=10, the multiplier is about 2.062713, giving ES 20.627128 loss units. The quantile multiplier instead gives the lower threshold 16.448536.
Keep other distributions and limits explicit
At zero dispersion, use the constant-loss limit rather than the density formula. A discrete model with threshold mass needs exact tail allocation. Neither equation estimates a market distribution or implements a stressed regulatory capital model.