In the current analysis, we have attempted to fit earthquake inter-event time data corresponding to the Himalayas and the adjacent regions, to various probability distributions. We have evaluated these models using two popular non-parametric tests. The gamma distribution was found to be the best fit among the applied models, with the shape parameter equal 0.8906 and a scale parameter equal to 635.324.
After completion of our analysis, the following significant results were noted:
- The AIC test established the exponential distribution (β = 565.93) as the best fit model for our data. The gamma distribution (α = 0.8906, θ = 635.324) comes a close second with an AIC value exceeding that of the former by a mere 1.3 units.
- The KS test established the gamma distribution (α = 0.8906, θ = 635.324) as the best fit model for our data, while the Weibull distribution (k = 0.9328, λ = 548.354) comes a close second, its value of the KS test statistic exceeding that of the former by a mere 0.013 units.
- All of the distributions, except the lognormal model estimated using the method of moments, have passed the KS goodness of fit test. The lognormal distribution is generally not the best alternative for this purpose; the results of our analysis have proven this.
- The models estimated using Maximum Likelihood Estimation have, in general, turned out to perform better than those estimated using Method of Moments.
While the Gamma and the Weibull distributions stand out as the best fitting models when evaluated using the KS test, they lose out to the exponential distribution (which is, essentially, a special case of the Gamma distribution), by a few points. Since the AIC test penalizes a model for an increase in its number of parameters, it assigns a slightly better score to the exponential distribution, due to the presence of just one parameter as opposed to two.
Aniruddha Jayant Karajgi
Ankit Sonthalia
Jatin Singh
Meet Kanani
Nayan Khanna
Rahul Jha
Rohit K Bharadwaj
Subham Kumar Dash
The final report can be found here.