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counter theory; Laplace transform; generating function; dead time
In the paper the authors investigate the explicit form of the joint Laplace transform of the distances between two subsequent moments f particle registrations by the Type II counter (the counter with prolonged dead time), in the general case, and the generating function of the number of particles arriving during the dead time. They give explicit solutions to the complicated integral equations obtained by L. Takács and R. Pyke, respectively. Moreover, they study the geometric behaviour of the distribution of the latter above mentioned random variable, and make some remarks on the Type II counter and the case of registration of $m$ types of particles.
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