Nile River minima series, 622 to 715 AD, Figure 327

tau_j Haar MODWT wavelet variance estimate
1.0   0.3587056451612904
2.0   0.2449464285714286
4.0   0.11129624640804592
8.0   0.04915869264240512

tau_j lower 95% confidence limit
1.0   0.2481418353873127
2.0   0.1476068624920634
4.0   0.05566960349555297
8.0   0.019067909083651403

tau_j upper 95% confidence limit
1.0   0.5643107570913821
2.0   0.48408885865821644
4.0   0.3233157249466867
8.0   0.30053220431513883

tau_j equivalent degrees of freedom (eta_3)
1.0   46.5
2.0   22.75
4.0   10.875
8.0    4.9375

percentage points from chi-square distribution
used to form lower 95% confidence limits
Q_{46.5}(0.975)   = 67.21886486398105
Q_{22.75}(0.975)  = 37.7525215014961
Q_{10.875}(0.975) = 21.741607694119555
Q_{4.9375}(0.975) = 12.729295270763663

percentage points from chi-square distribution
used to form upper 95% confidence limits
Q_{46.5}(0.025)   = 29.557849625218015
Q_{22.75}(0.025)  = 11.511380917639341
Q_{10.875}(0.025) =  3.7435441158548044
Q_{4.9375}(0.025) =  0.807637389393908