Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Question 1 (20 points in total). The following data are assumed to be an i.i.d. sample from a Cauchy(,1) distribution: 1.77, -0.23, 2.76, 3.80, 3.47,

Question 1 (20 points in total). The following data are assumed to be an i.i.d. sample from a

Cauchy(,1) distribution:

1.77, -0.23, 2.76, 3.80, 3.47, 56.75, -1.34, 4.24, -2.44, 3.29, 3.71, -2.40, 4.53, -0.07, -1.05, -13.87,

-2.53, -1.75, 0.27, 43.21

The density function of the Cauchy(,1) distribution is

f(x) = (1/)[(x)^2 +1]^1

(a) (2 points) Draw a dot plot of this dataset.

(b) (4 points) Plot the log likelihood function and the first derivative of the log likelihood function.

(c) (14 points) Find the MLE for using the Newton-Raphson method. Try with all of the

following starting points: -11, -1, 0, 1.5, 4, 4.7, 7, 8, and 38. Discuss your results. Is the mean

of the data a good starting point?

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Calculus Early Transcendentals Early Transcendentals

Authors: Dennis G Zill, Warren S Wright

4th Edition

0763797375, 9780763797379

More Books

Students also viewed these Mathematics questions

Question

In the context of capital budgeting, what is capital rationing?

Answered: 1 week ago