(a) Assume that the sample is from a distribution with density function f(x | σ) = 2 exp(-²¹). Note that here | x | denotes the absolute value of x. Please find the maximum likelihood estimate of o. (b) Assume that the sample is from the Pareto distribution, which has been used in economics as a model for a density function with a slowly decaying tail. The density function is given by f(x | x₁,0) = 0xx-0-1, * > 0,0 > 1. Here xo> 0 is given. Please find the maximum likelihood estimate of 0.
(a) Assume that the sample is from a distribution with density function f(x | σ) = 2 exp(-²¹). Note that here | x | denotes the absolute value of x. Please find the maximum likelihood estimate of o. (b) Assume that the sample is from the Pareto distribution, which has been used in economics as a model for a density function with a slowly decaying tail. The density function is given by f(x | x₁,0) = 0xx-0-1, * > 0,0 > 1. Here xo> 0 is given. Please find the maximum likelihood estimate of 0.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 25EQ
Related questions
Question
Assume a sample X1,X2 ,,Xn are i.i.d. random variables from a distribution given below.
![(a) Assume that the sample is from a distribution with density function f(x |
σ) = 2/1/2 exp (-2¹). Note that here | x | denotes the absolute value of x.
o)
20
σ
Please find the maximum likelihood estimate of o.
(b) Assume that the sample is from the Pareto distribution, which has been used
in economics as a model for a density function with a slowly decaying tail.
The density function is given by f(x | xo, 0)
0x8x-0-1
хох
* > £0,0 > 1.
Here xo> 0 is given. Please find the maximum likelihood estimate of 0.
=
9](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2ab050a-d13e-4a73-9fee-dc44d5d071e8%2Fa1d73c5c-293e-4148-8abc-6ceed75a50ee%2Fgkpqjsa_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Assume that the sample is from a distribution with density function f(x |
σ) = 2/1/2 exp (-2¹). Note that here | x | denotes the absolute value of x.
o)
20
σ
Please find the maximum likelihood estimate of o.
(b) Assume that the sample is from the Pareto distribution, which has been used
in economics as a model for a density function with a slowly decaying tail.
The density function is given by f(x | xo, 0)
0x8x-0-1
хох
* > £0,0 > 1.
Here xo> 0 is given. Please find the maximum likelihood estimate of 0.
=
9
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