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In this research we assumed that the number of emissions by time (𝑡) of radiation
particles is distributed poisson distribution with parameter (𝑡), where < 0 is the
intensity of radiation.
We conclude that the time of the first emission is distributed exponentially with
parameter 𝜃, while the time of the k-th emission (𝑘 = 2,3,4, … . . ) is gamma distributed
with parameters (𝑘, 𝜃), we used a real data to show that the Bayes estimator 𝜃
∗
for 𝜃 is
more efficient than 𝜃̂, the maximum likelihood estimator for 𝜃 by using the derived
variances of both estimators as a statistical indicator for efficiency