[R] (Interpretation) VGAM - FRECHET 3 parameters by maximum likelihood estimation for

[Maithili Shiva]

Dear R Helpers


This is the R code (which I have slightly changed) I got in VGAM package for estimating the parameters of FRECHET.

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y = rfrechet(n <- 100, shape=exp(exp(0)))       #    (A)

fit3 = vglm(y ~ 1, frechet3(ilocation=0), trace=TRUE, maxit=155)   #   (B)

coef(fit3, matrix=TRUE)                               #   (C)

Coef(fit3)                                            #   (D)

fitted(fit3)[1:5,]                                    #   (E)

mean(y)                                               #   (F) 

weights(fit3, type="w")[1:5,]                         #   (G) 
                             

vcov(fit3)                                            #    (H)    

fit3 at extra$location[1:3]  # Estimate of the location parameter  #    (I)
    
fit3 at extra$LHSanchor      # Anchor Point              #    (J)

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When I run these commands using R I get following output corresponding to each command line 


OUTPUT # (A)

[1]  0.7495887  1.1578511  0.8872487  0.7781103  1.1026540  1.8557026  1.1527270  1.1538885

[9]  1.0436005  0.8702552  1.0326653  1.1456378  1.1292287  0.9779141  0.7882611  2.0040318

[17]  0.8832376  1.6684632  0.7112340  1.8440806  0.8103669  0.6171517  0.6632612  0.9288173

[25]  1.2625774  1.2371949  2.3995687  0.9674406  1.2205647  2.2997349  1.3561988  1.0257294

[33]  0.7693035  1.3112102  1.2841138  0.5207330  0.8861406  0.7819666  1.1376008  1.3396068

[41]  0.6828540  0.7358596  0.8678724  1.1191930  0.9581007  0.8645687  1.0269345  0..9853376

[49]  0.7861684  2.2938797  0.5994656  1.3733527  3.0904095  2.7179989  0.8408945  0.9995262

[57]  1.0456575  0.6139744 17.4274447  0.5928158  1.6172649  0.7354806  1.4714551  0.7851852

[65]  1.9091740  1.0862915  1.9082128  1.0051395  1.0991948  1.6698645  2.8901334  0.8174091

[73]  1.3964180  0.7452934  0.8133906  1.2417527  2.1583672  1.1822409  0.8068691  0.8410480

[81]  1.2394454  1.3391757  1.0867579  1.3395385  1.2791401  0.7897431  1.2112373  1.6531473

[89]  1.7432403  6.7756058  0.9385585  1.5561437  0.9590773  0.7936483  2.5215168  1.1984615

[97]  0.6345925  1.4218795  2.3178357  1.5454827



OUTPUT # (B)

In vglm.fitter(x = x, y = y, w = w, offset = offset, Xm2 = Xm2,   :  convergence not obtained in 155 iterations.




OUTPUT # (C) 

> coef(fit3, matrix=TRUE)                               

                log(difference)	 log(scale)	 loglog(shape)
(Intercept)      -0.7954072	 -0.1283776  	 -0.03175329




OUTPUT # (D)

> Coef(fit3))

                 difference 	scale      	shape 
                  0.4513974  	0.8795212  	2.6346374

(IS IT THAT THESE GIVE THE SCALE AND SHAPE PARAMETER  ESTIMATES OF FRECHET.?)



OUTPUT # (E)

> fitted(fit3)[1:5,]          

[1] 1.339454  1.339454  1.33954  1.339454  1.339454


(WHAT DOES THIS MEAN?)



OUTPUT # (F)

> mean(y) 

[1] 1.439024



OUTPUT # (G) 	

weights(fit3, type="w")[1:5,]                                           
         

 [,1]    		 [,2]      		[,3] 		[,4]      		[,5]       		[,6]

[1,] 24.264915 	46.60547 	38.864660 	-33.624853 	40.492033 	-29.075460

[2,]  7.599936 	14.18608  	1.554636  	-9.724618  	2.440009  	-2.670739

[3,]  6.486803 	26.53437  	1.855081 	-12.926846 	-5.700736   	2.433455

[4,] 16.768849 	37.36856 	36.299447 	-25.025068 	34.078418 	-22.643518

[5,]  9.562077 	15.87083  	2.671884 	-11.625172  	4.418292  	-4.454716



(WHAT DOES THIS MEAN?)



OUTPUT # (H)

vcov(fit3)                                                      
                   (Intercept)1  (Intercept)2	 (Intercept):3
(Intercept) : 1	  0.0022605491   0.0021317673 	 -1.576056e-04
(Intercept) : 2	  0.0021317673   0.0020926942    -1.780387e-04
(Intercept) : 3	 -0.0001576056	-0.0001780387     3.892675e-05


Warning message:

In summaryvlm(object, corr = FALSE, dispersion = dispersion) :   the estimated variance-covariance matrix is usually inaccurate as the working weight matrices are a crude BFGS quasi-Newton approximation


OUTPUT # (I)	

fit3 at extra$location[1:3] # Estimate of the location parameter 

         1         	 2          		3 
0.06930899	 0.06930899 	0.06930899

(What does this MEAN? IS IT THAT 'D' gives SCALE and SHAPE parameter whereas this gives me LOCATION parameter?)



OUTPUT # (J)	

fit3 at extra$LHSanchor # Anchor point                                 

[1] 0.520733

(What does this mean?)



My problem is to calculate the estimators of 3 Parameter FRECHET distribution. Which of the above figures give me estimates of the three parameters of the FRECHET distribution.



With regards and thanking in advance,


Maithili




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