= Poisson record counts in cumulative hazard coordinates
{c}
{title2=$R_t\sim\operatorname{Poisson}(-\log(1-F(t)))$}
Upper records of iid observations with a continuous distribution have transition density $f(w)/(1-F(v))$ above the latest record $v$. Consequently the cumulative hazard $\Lambda(v)=-\log(1-F(v))$ transforms consecutive record increments into independent unit exponentials. Record counts below a level $t$ with $F(t)<1$ are therefore Poisson with mean $\Lambda(t)$. Set the count to zero if the first record exceeds the level. At a finite upper endpoint with $F(t)=1$, the count is infinite instead of a finite-mean Poisson variable.
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