By present work we are submiting a biometrical pattern appearing in many actuarial applications and consisting in a consideration of a group of N elements subject, in due course, to a stochastic diminution. Such a group will be considered as closed.
We approach in the first part thereof the problem of estimating the probability that from these N elements, in a certain steta at the origin of the system, would exist in a certainx moment number of elements having moved to two other stades whilst the other will remain at the starting state.
Every necessary assumptions are established and it is put the equation of the system. To get its solution we will use the generatrix function arriving at the fact that the latter will correspond to a multinomial distribution.
The average means of this distribution will depend on the elebentary probabilities of a state change. Considering that the assumtions must be made on the latter, owing to have got the essence of the phenomenon in study in its most elementary appearance.
Also the marginal process will be establisted in the event of a sole elimination cause.
In the second part an interpretation will be given within the dynamic statistics, as it will be dealt with a stochastic process the graphical representation of which would need a space of three dimensions.
In the third part some actuarial interpretations are given both of the marginal process and multinomial one.