Le Cam’s Procedure and Sodium Channel Experiments

Abstract

Consider a random variable U which has either a discrete distribution,

$$ \begin{array}{*{20}{c}} {P\left[ {U = 0} \right] = 1 - p,} \hfill \\ {P\left[ {U = u} \right] = p\left( {1 - \lambda } \right){{\lambda }^{u}}} \hfill \\ \end{array} $$

(1)

for u = 1, 2,…, with parameters 0 < p < 1 and $0 < \lambda < 1$ ,or a mixture distribution with an atom at zero and an exponential density for u > 0,

$$\begin{array}{*{20}{c}} {P\left[ {U = 0} \right] = 1 - p,} \hfill \\ {{\text{ }}p\lambda \exp \left( { - \lambda u} \right),} \hfill \\ \end{array}$$

(2)

for $\lambda > 0$