= Missing-pulse bias in average-power inference
\b[Missing-pulse bias in average-power inference] arises when a nominal trigger rate is used as though every trigger emitted a pulse. With background removed and complete pulses counted, let $M$ be the number of triggers and $N$ the number of emissions during $T$. Then
$$
\frac{\overline P}{M/T}=\frac NM\,\overline U_{\rm emitted}.
$$
The quotient is mean energy per trigger, including failed triggers as zero-energy outcomes. It equals the <conditional pulse-energy mean given emission> only when every trigger emits, or after correction for the measured emission fraction. Historical calorimetric inference uses energy, injection time and pulse rate; those quantities must describe the same collection.<Calibration Service for Laser Power and Energy at 248 nm by Rodney W. Leonhardt>[§6.2, Laser stability]{ref}
For an original five-trigger record, suppose energies are $0,1,0,3,0\,\mathrm{\mu J}$. Mean energy per trigger is $0.8\,\mathrm{\mu J}$, while the two emitted pulses average $2\,\mathrm{\mu J}$. At a nominal $1\,\mathrm{kHz}$ trigger rate, their average power is $0.8\,\mathrm{mW}$. The actual emission rate is $400\,\mathrm{Hz}$, consistent with the same power and emitted-pulse mean.
A pulse monitor with a threshold above the weaker pulse could detect only the $3\,\mathrm{\mu J}$ event. Its detected-event average would then be $3\,\mathrm{\mu J}$, also different from the true emitted-pulse mean. Failure to detect is not automatically failure to emit. A calibrated pulse-resolving receiver and a trigger counter distinguish emitted, detected and commanded events. The <average power of a laser pulse train> article additionally treats continuous backgrounds and observation-window accounting.
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