As can be seen in Figure 6, the P value for the slope of the fitted linear relation is given as 0.266. This means SB203580 molecular weight that there is a 0.266 probability of obtaining a slope estimate as extreme as or more extreme than the one obtained if the null hypothesis of no linear relation was true. As the P value is more than the level of significance, the null hypothesis of no linear relation is accepted.Figure 6Annual total rainfall versus time for the data obtained from the weather station of Kuwait International Airport for the time duration from 1965 (corresponding to year number 1) to 2009 (year number 45). The solid line represents a trend fitted for the …The periodic pattern of monthly rainfall data can now be estimated from the detected periods in the previous section.

In general, a time-based data containing a periodic sinusoidal component with a known wavelength can be modeled using Fourier series, which can be expressed for multiperiods ass(t)=��n=1�ޡ�i=1kRn,icos??(2n��fit+��n,i),(2)whereRn,i=an,i2+bn,i2,��n,i=tan?1?(?bn,ian,i),an,i=2fi��LiLi+1/fif(x)cos??(2n��fit)dx,bn,i=2fi��LiLi+1/fif(x)sin??(2n��fit)dx,(3)where s is periodic sinusoidal component of rainfall; R is amplitude of variation; f is frequency, equal to the inverse of period; �� is phase angle; and k is total number of periodicities. The term (2n��ft + ��) is measured in radians. As determined from the data, k value is equal to eight, and the values of f may be set by the periodic nature of rainfall data, that is, f1 = 1/6, f2 = 1/12,�� cycles per month.

The phase angle, ��, is necessary to adjust the model so that the cosine function crosses the mean, which is equal to zero for the data, at the appropriate time t. The difficulty is to determine analytically the function f(x) in Fourier coefficients. However, because of the existing randomness, a more simple procedure may be followed by determining ��n,i and Rn,i by means of numerical optimization. Since the above equation will not be solved analytically, it is more convenient to reduce the number of fitting coefficients. This is achieved by testing a number of s(t) models each obtained by assuming a different value of n. Based on Fourier procedure, the larger n value considered, the higher model accuracy obtained. In this case, however, a higher accuracy would result with a more complicated model form because of the many periods detected in the data.

Accordingly, it can be considered for simplicity n = 1. One difficulty remains is that a cosine function crosses a mean equal to zero will produce positive and negative values. In reality, there should be only positive values, while the negative ones should correspond to zero rainfall. To produce zero rainfall, the binary model is usedF(t)={s(t)if??s(t)��0,0if??s(t)<0.(4)Following Anacetrapib the above procedure, a model of s(t) is obtained with coefficients shown in Table 1. The overall rainfall model F(t) is presented in Figure 4(b).