Parametric Approximations Gauss file(s) npd_parametric.g Matlab file(s) npd_parametric.m Simulate T = 200 random numbers from a normal distribution f(y; ) = 1 22 exp

Parametric Approximations Gauss file(s) npd_parametric.g Matlab file(s) npd_parametric.m Simulate T = 200 random numbers from a normal distribution f(y; θ) = 1 √ 2πσ2 exp  − (y − µ) 2 2σ 2  , with parameters µ = 0 and σ 2 = 9.

(a) Estimate the population distribution using a normal distribution parametric density estimator where the mean and the variance are estimated as y¯ = 1 T X 200 t=1 yt s 2 = 1 T − 1 X 200 t=1 (yt − y¯) 2 .

(b) Estimate the population distribution using a Student t parametric density estimator where the mean and variance are computed as in

(b) and the degrees of freedom parameter is computed as ν = 2s 2 s 2 − 1 .

(c) Plot the parametric density estimates and compare the results with the normal distribution, N(0, 9).