deletions | additions       diff --git a/In_any_physical_theo.tex b/In_any_physical_theo.tex  index 5fb68db..ed103c8 100644  --- a/In_any_physical_theo.tex  +++ b/In_any_physical_theo.tex 
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In any physical theory the rate of signal events is non-negative, thus $\mu\ge 0$. However, it is often convenient to allow $\mu<0$ (as long as the pdf $f_c(x_c | \mu,\vec\theta)\ge 0$ everywhere). In particular, $\hat\mu<0$ indicates a deficit of events signal-like with respect to the background only and the boundary at $\mu=0$ complicates the asymptotic distributions. Ref.~\cite{asimov} uses a trick that is equivalent to requiring $\mu\ge 0$ while avoiding the formal complications of a boundary, which is to allow $\mu< 0$ and impose the constraint in the test statistic itself. In particular, one defines $\tilde \lambda(\mu)$  \begin{equation}  \label{eqn:lambdatilde} \begin{equation}\label{eqn:lambdatilde}  \tilde{\lambda}({\mu}) = \left\{ \begin{array}{ll} \frac{ L(\mu, \hat{\hat{\vec{\theta}}}(\mu)) }  {L(\hat{\mu}, \hat{\vec{\theta}}) } & \hat{\mu} \ge 0 , \\*[0.3 cm]  \frac{ L(\mu, \hat{\hat{\vec{\theta}}}(\mu)) } {L(0,