1、Case Study Gumbel Distribution,Rhone River Maximum Daily Discharge (Annual) 1826-1936Data Source: E. Gumbel (1941). “The Return Period of Flood Flows,” The Annals of Mathematical Statistics, Vol. 12,#2, pp.163-190.,Data,Years 1826-1936: maximum daily discharge of river obtained.,Gumbel Distribution,
2、Maximum Likelihood Estimation (I),Maximum Likelihood Estimation (II),Maximum Likelihood Estimation (III),Step 1, choose starting values, say: a(0) and b(0) are assigned the method of moment estimators Step 2: Choose a tolerance level for the change is estimates, say k=10-6 Step 3: Obtain H-1(a(0), b
3、(0) and f(a(0), b(0) Step 4: Obtain a(1) and b(1) from Newton-Raphson algorithm Step 5: Check to see if (a(1)- a(0)2+ (b(1)- b(0)2 k. If Yes, Stop. If No, Return to Step 3, obtaining H-1(a(1), b(1), f(a(1), b(1),Rhone River Discharge Data,Rhone River Discharge Data (2),Iteration History:,Rhone River Discharge (3),Rhone River Discharge Data (4),
