Question

4. Let XI, . .. , Xn be a random sample from the inverse Gaussian distribution. IG(μ, λ), whose pdf is (a) Show that the MLE of μ and λ are μ-X and (b) It is known that nA/λ ~ χ2-1. Use this to derive a 100-(1-a)% CI for λ (c) (R) Consider the following dataset 10.6, 91.3, 51.7, 2.2, 3.8, 6.0, 17.8, 131.8, 31.0, 4.2, 13.7, 10.2, 9.9, 4.3, 5.6, 12.9, 42.0, 14.1, 3.8, 9.3, 2.6, 27.6, 1.7, 7.0, 2.1, 1.5, 7.5, 2.5, 2.4, 51.9 (i) Assuming an inverse Gaussian distribution is an appropriate model for these data, compute the maximum likelihood estimate of λ and give a 95% CI (ii) Draw a QQ plot to compare these data to the fitted inverse Gaussian distri- bution, IG(, A). Is this model appropriate for these data? Hint: Quantiles for the inverse Gaussian distribution may be computed using the qinvgauss function in the statmod R package.

NOTE: DO PART c) ONLY

PLEASE INCLUDE THE R CODES ALONG WITH THE PLOTS

Answer 1

Consider the Pollowing dataset soly i) Assuming an inveese Gaussian distribution is an approptiate Mod pułe the Maximum likelihood estimate of λ and give a g5 % CI el for these ddta Com so we have n - 32 and 5- 21.2G5025 Σ(x-2) = 4.4223362 32 4 223362 X - 7-23431634 Thus the MLE estimele op X is 7-23431634 I Peom the table we have 0.915 ะเ7-53873858 o 02531 48 23188959 Thus the value of the Confidence intervalis 2.320 , logos i) Draw a aa Plot to Compare these dała to the Is this Model appropriale Por these datq Pitted invesse Giaussian distribution Ii(AA) The Code to be used in R (P Mean -) shape Null , dispets i on-l , lowe fail-Eye teace = FALSe OEtry Putting g in vgak less (x,u,t) here you should get the tequised plot using will be yo vecto of values the Commend