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Official Journal of the Asia Oceania Geosciences Society (AOGS)

Table 2 Asymptotic standard deviations and 90% CI of model parameters

From: Nowcasting earthquakes in Sulawesi Island, Indonesia

Model1 Parameter values Asymptotic standard deviation2 Confidence interval2 (90%)
Lower Upper
Exponential \(\hat{\alpha }\) 191.9540 \(\sigma_{{\hat{\alpha }}}\) 20.5796 158.1006 225.8074
Gamma \(\hat{\alpha }\) 231.1659 \(\sigma_{{\hat{\alpha }}}\) 39.2204 166.6483 295.6835
\(\hat{\beta }\) 0.8304 \(\sigma_{{\hat{\beta }}}\) 0.1068 0.6547 1.0061
Weibull \(\hat{\alpha }\) 191.0590 \(\sigma_{{\hat{\alpha }}}\) 21.9706 154.9174 227.2006
\(\hat{\beta }\) 0.9888 \(\sigma_{{\hat{\beta }}}\) 0.0825 0.8531 1.1245
  1. 1For the exponentiated exponential model, the parametric uncertainties cannot be computed as the trigamma function \(\psi ^{\prime}\left( {\beta - 1} \right)\) is not defined for \(\hat{\beta } < 1\) (see Pasari and Dikshit 2015, 2015a, 2015b; Pasari 2018)
  2. 2For the computation of asymptotic standard deviation and 90% confidence interval of the model parameters, we followed a surrogate approach of Fisher Information Matrix and associated Cramer–Rao lower bound theorem (see Pasari and Dikshit 2015, 2015a, 2015b; Pasari 2018)