Let 
and 
be the probabilities of occurrence for
wet and dry series of length 
and 
, associated with day 
. The
distribution may be approximated by the geometric distribution
with the parameter obtained from observation data by the maximum likelihood
method. The distribution is approximated by mixing of two
geometric distributions with the probability p for short series (shorter than
one week) and the probability 1-p for long series.
The distribution of precipitation (in mm) is a mixing of three distributions:
Here 
, 
and 
are the probabilities of
``small'' (less than 0.5 mm), ``medium'' (0.5 - 20 mm) and ``large''
(more than 20 mm) precipitation for each (
). UNI is the uniform
distribution for small precipitation, EXP is the exponential distribution for
medium precipitation and 
is the mean large precipitation.
The temperature is described by a normal distribution with different parameters
for wet and dry series, so that
where 
is the correlation coefficient between
two consecutive days, N(0,1) is the Gauss function with parameters 0 and 1,
a and b (
) are the parameters providing the standard normal
distribution for 
. The index l points the position of day within
the series, the index k stands for w-wet and d-dry series. In this way
the daily temperature is defined for each by its arithmetic mean,
, and its variance, 
.
Solar hours are also described as a normal stochastic variable with the
parameters depending on the number of day, , and its position within
either wet or dry series, l.
As an illustration, one result of calculation with help of our generator is shown in Fig. 4.
Figure 4: Probabilities of the following events: a) minimal temperature
exceeds a given value within the period from day 120 to 240 ; b) maximal
temperature exceeds a given value within the period from day 20 to 240.
Since the functional dependence is very unwieldy for descriptive presentation of calculation results we shall try to compress these distributions to a few moments of them. Thus, each trajectory will be described by two values: mean and variance calculated for the vegetation period, and then the crop yield will be a function of six variables. At the beginning we suppose that crop production depends on two variables only: annual (more correct, vegetation period) mean temperature and temperature variance.