Consider thefamilyofgammadistributionswithidenticalparameters for shapeandscale,i.e.withdensities with respecttostandardLebesguemeasureon R+ as inExercise3.7.Showthatthe MLE of is uniqueandwell-definedasasolutiontothescoreequation. Hint: Use that

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Consider thefamilyofgammadistributionswithidenticalparameters for shapeandscale,i.e.withdensities

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with respecttostandardLebesguemeasureon R+ as inExercise3.7.Showthatthe MLE of β is uniqueandwell-definedasasolutiontothescoreequation. Hint: Use that the trigamma function Ψ1(β) = D2 log Γ(β) is strictlypositiveon R+.

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Fundamentals Of Mathematical Statistics

ISBN: 9781032223827

1st Edition

Authors: Steffen Lauritzen

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Consider thefamilyofgammadistributionswithidenticalparameters for shapeandscale,i.e.withdensities with respecttostandardLebesguemeasureon R+ as inExercise3.7.Showthatthe MLE of is uniqueandwell-definedasasolutiontothescoreequation. Hint: Use that

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fs(x)= 28-1-1/8 T(B)BB BER+

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Fundamentals Of Mathematical Statistics

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