RIVARD and BLEDSOE: PARAMETER ESTIMATION FOR PELLA-TOMLINSON MODEL 



hounds (Table 3). Out of the 20 cases considered, 

 the true parameter vahie lay outside the arbitrary 

 ±2 (SDl confidence interval only once tor ru and/?. 



Also, variance estimates were comparable with 

 the variance estimates of the five-parameter pro- 

 cedure (compare Tables 2 and 3). 



Table 2. — Estimated parameters for the deterministic model and for 18 stochastic replicates. The 

 Levenberg-Marquardt algorithm is employed in a five-dimensiona! parameter space i m ,By.,n,q,Bg). For each 

 parameter and replicate, the parameter estimate ± its estimated standard deviation from Equation ( 12) are 

 tabulated. Replicates 13 and 15 have been e.xcluded due to degeneracy of the model, as discussed in the text. 



',r =S(«) (r-5), 



^For 10 replicates with rr = 0,200 



^Overall standard deviation of parameter estimates for 10 replicates with ir ^- 200 



Table 3. — Estimated parameters for 20 stochastic replicates of the deterministic 

 model. The Levenberg-Marquardt algorithm is employed here in a three- 

 dimensional parameter space (w, q, n). For each parameter and replicate, the 

 parameter estimate ± its estimated standard deviation from Equation (12) are 

 tabulated. 



'(> = S (6) (r-3). 



^For 12 replicates with -r = 200 



^Overall standard deviation of parameter estimates for 12 replicates with u = 0.200. 



529 



