*05. V0605. Gasqui. Individual

particular, the period factor. The exponential
relation warrants that the hazard calculated
this way be positive. The parameter 
β
is
the vector of the model coefficients related
to the various factors that weight on the Ren
hazard through the similar relation
λ
r
=
exp(X
2
·
β
), where X
2
is the associated inci-
dence vector. The parameter 
α
is the vec-
tor of the model coefficients that reflect the
effects of the various factors weighting on
the Ren rate through the relation: p =
exp(X
3
·
α
)/[1 + exp(X
3
·
α
)], where X
3
is the
associated incidence vector. This latter rela-
tion warrants a p value between 0 and 1,
which clearly fits the variation range of
probability. This total likelihood therefore
solely depends on unknown coefficients 
θ
,
β
and 
α
so defined. Maximising the full
likelihood according to the unknown coef-
ficients of the model will provide estimates
of these coefficients.
Given the parameters of the model, Rex
hazard and Ren hazard and rate, the proba-
bility law of the random number of mastitis
over any lactation duration from calving can
be expressed; the probability formulas are
given in Appendix II. Again in this model,
the clinical mastitis count over the whole
lactation does not have a Poisson distribu-
tion.
The interest of the proposed approach
was that it also provides an estimator of the
distribution function for occurrence time of
the wth mastitis from the calving date,
P(T
w
≤
t) for any occurrence time t > t
0
,
based on parameter estimators. Indeed,
P(T
w
≤
t) = P(N(t
0
,t) 
≥
w) = 1 – P(N(t
0
,t)
< w) can be deducted from the recurrence
formulas of Appendix II.