All models' residuals conform to
standard normal distribution. In the verification sample, the agreement rate of normal values was over 90%; except for females' VC and FEV[sub]6 and males' FEV[sub]1/VC, the agreement rate for these three parameters was all 88%.
The symmetric distributed source signals are generated based on the
standard normal distribution. The M x N mixing matrix is generated randomly, whose entries are subject to the
standard normal distribution.
For a constant [eta] [member of] (0,1), let [z.sub.n] denote the [eta]th upper-quantile of
standard normal distribution. For example, if [eta] = 0.1, then [z.sub.n] = 1.2816, which means that for a random variable with
standard normal distribution, it is greater than 1.2816 with 10% probability.
where [mathematical expression not reproducible] is an expectation operator with respect to [mathematical expression not reproducible] and [PHI](x) is cdf of the
standard normal distribution.
The improper model error may be generated when a single
standard normal distribution approximation is used, so Gaussian mixture distribution approximation is proposed.
It can be achieved by two steps: the first step is to generate the
standard normal distribution series by exchanging the random variables of sobol sequence which obeys the U (0, 1) distribution; the second step is to exchange the
standard normal distribution into the corresponding normal distribution based on the mean and variance of necessary
standard normal distribution series.
We then can take a critical value from the
standard normal distribution at a 10 % significance level to determine if a particular model performs significantly better in explaining the data than another.
Figure 1 illustrates a
standard normal distribution with a mean of zero and a standard deviation of one.
Since the fluctuation of demands has a stochastic character, the possible results are random variables equivalent to the
standard normal distribution. Figure 4 shows that if the demand is a random variable, the occurrence of extreme demands has a very low probability, thus the stock shortage can be most likely avoided only with a safety stock with an infinite high level.