Recurrence statistics of M ≥ 6 earthquakes in the Nepal Himalaya: formulation and relevance to future earthquake hazards

Recurrence statistics of large earthquakes has a long-term economic and societal importance. This study investigates the temporal distribution of large (M ≥ 6) earthquakes in the Nepal Himalaya. We compile earthquake data of more than 200 years (1800–2022) and calculate interevent times of successive main shocks. We then derive recurrence-time statistics of large earthquakes using a set of twelve reference statistical distributions. These distributions include the time-independent exponential and time-dependent gamma, lognormal, Weibull, Levy, Maxwell, Pareto, Rayleigh, inverse Gaussian, inverse Weibull, exponentiated exponential and exponentiated Rayleigh. Based on a sample of 38 interoccurrence times, we estimate model parameters via the maximum likelihood estimation and provide their respective confidence bounds through Fisher information and Cramer–Rao bound. Using three model selection approaches, namely the Akaike information criterion (AIC), Kolmogorov–Smirnov goodness-of-fit test and the Chi-square test, we rank the performance of the applied distributions. Our analysis reveals that (i) the best fit comes from the exponentiated Rayleigh (rank 1), exponentiated exponential (rank 2), Weibull (rank 3), exponential (rank 4) and the gamma distribution (rank 5), (ii) an intermediate fit comes from the lognormal (rank 6) and the inverse Weibull distribution (rank 7), whereas (iii) the distributions, namely Maxwell (rank 8), Rayleigh (rank 9), Pareto (rank 10), Levy (rank 11) and inverse Gaussian (rank 12), show poor fit to the observed interevent times. Using the best performed exponentiated Rayleigh model, we observe that the estimated cumulative and conditional occurrence of a M ≥ 6 event in the Nepal Himalaya reach 0.90–0.95 by 2028–2031 and 2034–2037, respectively. We finally present a number of conditional probability curves (hazard function curves) to examine future earthquake hazard in the study region. Overall, the findings provide an important basis for a variety of practical applications, including infrastructure planning, disaster insurance and probabilistic seismic hazard analysis in the Nepal Himalaya.