Consider a random sample X1,...,Xn (n > 2) from Beta(θ,1), where we wish to estimate the parameter θ. (a) Find the MLE θˆ and write it as a function of T = − ∑ni=1 log Xi. (b) Find the sampling distribution of T = − ∑ni=1 log Xi . (Hint: First find the distribution of Ti = − log Xi .)

Consider a random sample X1,...,Xn (n > 2) from Beta(θ,1), where we wish to estimate the parameter θ. (a) Find the MLE θˆ and write it as a function of T = − ∑ni=1 log Xi. (b) Find the sampling distribution of T = − ∑ni=1 log Xi . (Hint: First find the distribution of Ti = − log Xi .)

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 56SE: Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such...

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Question

Consider a random sample X₁,...,X_n (n > 2) from Beta(θ,1), where we wish to estimate the parameter θ.
1. (a) Find the MLE θˆ and write it as a function of T = − ∑ⁿ_i=1 log X_i.
2. (b) Find the sampling distribution of T = − ∑ni=1 log Xi .
  
  (Hint: First find the distribution of Ti = − log Xi .)

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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