As shown in Fig. 1, the probability density curve obtained according to the probability density data points
is also shown. The probability density functions that are fitted are described by
p ¼ 2:7893^23:1228^ þ 1:6316 for the whole day period
p ¼ 2:2173^20:1827^ þ 0:3522 for the 08 : 00–20 : 00 period
3.2. The generation of hourly ambient temperature
As stated in the beginning of this paper, the objective of this study is to generate the hourly ambient tem-
perature needed for bin weather data generation in the case that only the daily maximum and minimum tem-
peratures are known. To do this, we can use the obtained probability density function to generate the
normalized hourly ambient temperature and then transform it to hourly temperature. This belongs to the
problem of how to simulate a random variable with a prescribed probability density function and can be done
on a computer by the method described in the literature [13]. For a given probability density function f ð^Þ, if
its distribution function F ð^Þ can be obtained and if u is a random variable with uniform distribution on [0, 1],
then
F, we need only set
As stated above, the probability density function of the normalized ambient temperature was fitted using a
one year long hourly temperature data. Based on the probability density function obtained, the random nor-
malized hourly temperature can be generated. When the daily maximum and minimum temperature are
known, the normalized hourly temperature can be transformed to an actual temperature by the following
equation
When the hourly temperature for a particular period of the day has been generated using the above method,
the bin data can also be obtained. Because the normalized temperature generated using the model in this study
is a random variable, the bin data obtained from each generation shows some difference, but it has much sim-
ilarity. To obtain a stable result of bin data, the generation of the bin data can be performed enough times,
and the bin data can be obtained by averaging the result of each generation. In this paper, 50 generations were
averaged to generate the bin weather data.
Z. Jin et al. / Energy Conversion and Management 47 (2006) 1843–1850
3.4. Methods of model evaluation
The performance of the model was evaluated in terms of the following statistical error test: