Question

Let For each of the following two sets of 10 observations from the given distribution, calculate the value of the maximum likelihood estimate and the method-of-moments estimate.

f (z , Ꮎ = Ꮎ1-1,0 < Ꮖ < 1, Ꮎe? = {Ꮎ : 0 < Ꮎ < x} .

1. 0.55, 0.20, 1.00, 0.83, 0.89, 0.28, 0.64, 0.36, 0.95, 0.54

The maximum likelihood estimator:

The method-of moments estimator:

2. 0.42, 0.11, 0.05, 0.83, 0.19, 0.31, 0.66, 1.00, 0.84, 0.57

The maximum likelihood estimator:

The method-of moments estimator:

Answer 1

. Ō Oti f(x)= 5 *. f (x; 0) dx = 5 o x dx = Q S x® dze = [x®+] for method or moments estimator; we nevee, € (X) = Ã - D obozoa + 8 = =) 0 (1-x) = a - o - - LOMME cs Scanned with CamScanner Q*1?



10). Corregedores f (n; jo) llo) = lop LW) = n lng a + i lop (ni ºy) z n log o + (0-1) À long si . in logo to the log ni se log ni do 640) = + log (601) so 1 Bls 1 -5.9185 116 10. OMR = - 80 [169]. Owne z Mad 11.667. . Smeer - 20.476). 0.624 1-0.624 OMME lo 0.976 MLE = -lo.241 0992 0.498 OMME 2 Scanned with 10.498 – Cara Seamer