Nile River minima series, 716 to 1284 AD, Figure 327

tau_j Haar MODWT wavelet variance estimate
1.0   0.1361048855633803
2.0   0.11027058303886932
4.0   0.09463330738434166
8.0   0.08112594835852874

tau_j lower 95% confidence limit
1.0   0.11622547655958651
2.0   0.08849248961357149
4.0   0.06974781020045244
8.0   0.0532612696076701

tau_j upper 95% confidence limit
1.0   0.16158878118466158
2.0   0.14125550524722372
4.0   0.1357671834210268
8.0   0.13849102572700053

tau_j equivalent degrees of freedom (eta_3)
1.0   284.0
2.0   141.5
4.0    70.25
8.0    34.625

percentage points from chi-square distribution
used to form lower 95% confidence limits
Q_{284.0}(0.975)  = 332.57585724058504
Q_{141.5}(0.975)  = 176.32329667903295
Q_{70.25}(0.975)  =  95.31467474955761
Q_{34.625}(0.975) =  52.73974846272794

percentage points from chi-square distribution
used to form upper 95% confidence limits
Q_{284.0}(0.025)  = 239.21083639975572
Q_{141.5}(0.025)  = 110.4614469552271
Q_{70.25}(0.025)  =  48.96610267839143
Q_{34.625}(0.025) =  20.28280133798165