Question

Q3. (40 pts) We know that a population of values (?) has a ?????(?, ?) distribution. We also know that ??? of the ?????(?, ?) distribution is defined properly as: ?(?) = ( ? ? ) ? ? (1 − ?) ?−? , ? = 0,1,2 … , ? ; ? ∈ ? + First reveal and write the properties of ?. Then, supposing a random sample of {?? } ?=1 ? is available, derive the ???ℎ?? ?? ??????? (??) estimator of distributional parameters ? and ?. Explain whether you require any specific features for your sample so that you will be able to obtain numerically consistent estimates. Show every element of your way of thinking explicitly. Show your formulas and calculations clearly in writing. Excel outputs are not accepted. Irrelevant elements in answer may cause severe loss of points.

Answer 1