252 S. Chauhan Fig. 23.10 Q–Q plot for one of the estimated modal frequencies (Case 1) Fig. 23.11 Q–Q plot considering modal frequency and damping as bivariate variable (Case 1) with the sampling distribution, which in absence of bias is most likely to be centered around population mean. This can be observed from Fig. 23.12 where histograms of frequency and damping estimates of 3nd mode (Case 1) from MPUQ-b and Monte Carlo are plotted on top of each other for illustration. The histograms have been normalized such that they plot an estimate of the probability distribution function of the estimates. Expectedly, the histograms look very similar in shape and spread. However, they don’t overlap each other completely, which is again on expected lines. This is more evident in damping histograms in comparison to frequency histograms. These histograms also look normal in terms of distribution and a normality check by means of Shapiro-Wilk’s normality test [18] reveals that the estimates have univariate normal distributions at significance level 0.05. Note that the figures also show the normal distribution characterized by mean and standard deviation of estimated bootstrap parameters i.e. !BS, BS! and BS, BS on top of the histograms. This again provides a quick visual impression about how closely the histograms follow normal distribution.
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