Question

Let X ~ IG (? : (?, ?)), ? ? > 0 and ? > 0. This means the random variable X follows the inverse Gaussian distribution with the set (? : (?, ?)) acting as the parameters of said distribution. Given that we observe a sample of size n that is independently and identically distributed from this distribution (i.i.d), x = (x?, ..., x?), please find the maximum likelihood estimate for ? and ?, that is ???? and ????. The probability density function (PDF) is as follows: f(x | ?, ?) = {? (? / 2?x³)¹/² e^(-?(x-?)² / 2?²x), x > 0; 0, x ? 0}

          Let X ~ IG (? : (?, ?)), ? ? > 0 and ? > 0. This means the random variable X follows the inverse Gaussian distribution with the set (? : (?, ?)) acting as the parameters of said distribution. Given that we observe a sample of size n that is independently and identically distributed from this distribution (i.i.d), x = (x?, ..., x?), please find the maximum likelihood estimate for ? and ?, that is ???? and ????. The probability density function (PDF) is as follows:

f(x | ?, ?) = {? (? / 2?x³)¹/² e^(-?(x-?)² / 2?²x), x > 0; 0, x ? 0}

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Let X IG (? : (?, ?)), ? ? > 0 and ? > 0. This means the random variable X follows the inverse Gaussian distribution with the set (? : (?, ?)) acting as the parameters of said distribution. Given that we observe a sample of size n that is independently and identically distributed from this distribution (i.i.d), x = (x?, ..., x?), please find the maximum likelihood estimate for ? and ?, that is ???? and ????. The probability density function (PDF) is as follows:

f(x | ?, ?) = ? (? / 2?x³)¹/² e^(-?(x-?)² / 2?²x), x > 0; 0, x ? 0

Added by Albert S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Areen Dabadghav

05/14/2023

Step 1

However, it appears you're asking about finding the maximum likelihood estimators (MLEs) for the parameters of an Inverse Gaussian (IG) distribution, given a sample. The Inverse Gaussian distribution is often parameterized by its mean (\(\mu\)) and shape parameter Show more…

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Let X ~ IC( : (, )), V > 0 and 1 > 0. This means the random varible X follows the inverse Gaussian distribution with the set (0 : (, )) acting as the parameters of said distribution. Given that we observe a sample of size n that is independently and identically distributed from this distribution (i.i.d), x = (x1, ... , x,), please find the maximum likelihood -2(x-)2 2 e 22x x>0 f(xu,1) /.TT4 0, 0> x

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