# Table 3 Estimated parameter values along with their asymptotic standard deviations and confidence bounds

Model Parameter values Asymptotic standard deviation Confidence interval (95 %)
Lower Upper
Exponential α 13.346380 σ α 3.566970 6.355119 20.337641
Gamma α 11.312436 σ α 4.725639 2.050184 20.574688
β 1.179797 σ β 0.398276 0.399176 1.960418
Lognormal α 2.167443 σ α 0.271801 1.634713 2.700173
β 1.013243 σ β 0.191485 0.637932 1.388554
Weibull α 14.173818 σ α 3.347283 7.613143 20.734493
β 1.191600 σ β 0.248309 0.704914 1.678286
Levy α 5.089593 σ α 1.923685 1.319170 8.860016
Maxwell α 9.953759 σ α 1.086044 7.825113 12.082405
Paretoa α 1.169863 σ α 0.232367 0.714424 1.169863
β 0.497375 σ β 0.174958 0.154457 0.840293
Rayleigh α 12.190815 σ α 1.629066 8.997846 15.383784
Inverse Gaussian α 13.346380 σ α 4.543217 4.441675 22.251085
β 8.226885 σ β 3.109476 2.132312 14.321458
Inverse Weibull α 5.169580 σ α 1.499738 2.230094 8.109066
β 0.970010 σ β 0.202133 0.573829 1.366191
Exponentiated exponential α 0.089602 σ α 0.007673 0.074563 0.104641
β 1.336289 σ β 0.368175 0.614666 2.057912
Exponentiated Rayleighb α 22.635345
β 0.463758
Exponentiated Weibullb α 15.964143
β 1.319327
γ 0.847971
1. aFor Pareto distribution, we calculated (Quandt 1966) exact standard deviations (σ α , σ β ) of the estimated parameters; also, the upper confidence bound is capped at 1.169863, as α < t
2. bThe parametric uncertainties of exponentiated Rayleigh and exponentiated Weibull distributions are not calculated, as the FIMs are not completely known (Pal et al. 2006)