Psychometric function with guessing and lapses ($p(x)=\gamma +(1-\gamma -\lambda )F(x)$)

An empirical psychometric function whose core $F$ ranges from zero to one, lower asymptote is $\gamma$, and upper asymptote is $1-\lambda$. If $F(\alpha )=1/2$, then $p(\alpha )=\gamma +(1-\gamma -\lambda )/2$. A location parameter is consequently not a task-independent threshold. For a two-choice observer randomly guessing on fraction $r$ of otherwise perfect easy trials, the upper error asymptote is $r/2$, not $r$.