Two likelihood distributions, Weibull and lognormal, are applied to suit the annually wind pace info. The estimates of the product parameters and the corresponding requirements KS and AE for every fitting are outlined in Table two. In the present examine, the judgement criterion KS or AE reveal how a theoretical chance density operate matches with the observed wind pace distribution, where a scaled-down KS or AE implies a far better fitting. In the northern location, the lognormal distribution performs greater than the Weibull distribution in fitting annually wind speeds for most stations, apart from for Xingcheng station. Fig 6 compares the theoretical chance density capabilities with the observed wind speed histograms of annually wind speeds for 4 stations in the northern area. Therein, the corresponding cumulative distribution capabilities are also plotted for comparison. In Fig 6, the Weibull distribution is noticed to be constant with observed distribution of wind speeds for Xingcheng station. In Fig 6A, 6C and 6D, the lognormal distribution is nearer to the noticed distribution than the Weibull distribution.
In the southern location, we locate that the Weibull distribution performs greater in fitting annually wind speeds for Shengshi, Dachendao, and Xisha stations whilst for the other three stations, the lognormal distribution performs better in terms of the criteria KS and AE. Fig 7 displays the equipped probability density functions and the observed likelihood distribution of annually wind speeds for 4 stations in the southern area. The once-a-year maximum intense wind speeds at a 10-m height are equipped to the Gumbel distribution and the GEV distribution. The believed values of parameters are shown in Desk 3. Figs eight and nine assess the likelihood density distributions of the Gumbel distribution and the GEV distribution with the empirical distribution for stations in the northern area and southern area, respectively. From Figs eight and nine, the Gumbel distribution and GEV distribution are almost the very same for the Changhai, Xingcheng, Chengshantou, Qingdao, Shengshi, Dachendao, Nanao, and Shangchuandao stations.
The estimate of the shape parameter ε also verifies this end result. The probability ratio test even more reveals that the variances in between the equipped Gumbel distribution and the GEV distribution are not important, except for the Lvshi station . The Gumbel distribution and GEV distribution are nested likelihood distributions, the place the Gumbel is the simpler one particular with less parameters. In most cases, the Gumbel distribution is capable of describing the distribution of the intense wind velocity nonetheless, we uncover that the GEV distribution product is greater than the Gumbel distribution in this research. Employing the statistical deal R, the fitting of the empirical knowledge to GEV distribution is not as complicated as fitting to the Gumbel distribution.
