We assume that it is possible to apply gamma-distribution for describing
cooperation of the abovementioned enterprises during a specified time interval of
statistical research [3]. For developing this model, we consider the stream of events
with a constant intensity
(consumption of raw materials in conventional units of
value per hour); a random value X is time
0
t (in hours) necessary for supplying
a specified amount of events
(volume of supply of raw materials).
We set a gamma-distribution by a differential function:
(
)
()
1
,
0,
,,
0,
0 ,
t
Г
t
e
t
Г
ft
t
−−
=
(1)
Where the gamma-function is determined by an improper integral:
()
,
x
Г
x
edx
−−
=
1
0
0
, (2)
Which is uniformly convergent for all
0
. If
0
, then the gamma-function
has the continuous derivative and Г (1) = Г (0) = 1. According to the Rolle Theorem,
there is a point
within the internal (1, 2), where
()
Г
=0
. The gamma-function has
the minimum Г (1,461632...) = 0,885603 in this point (Figure 5).
Figure 5. Gamma-function graph
Figures 6 and 7 demonstrate graphs of the differential gamma-distribution
function for fixed values
1
=
і
2
=
responsively and for different values of
. If
grows and
1
=
, the value of maximum of the differential function decreases and
moves right (Figure 6); if
2
=
, then the curve configuration is close to the exponential
distribution (Figure 7).
1
1
2
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