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Recovering Fisher-Information from the MGF Alone without Requiring Explicit PMF or PDF from a One-Parameter Exponential Family

Author:

Nitis Mukhopadhyay

University of Connecticut, Storrs, CT 06269-4120, US
About Nitis
Department of Statistics
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Abstract

It is well-known that a finite moment generating function (m.g.f.) corresponds to a unique probability distribution. So, an important question arises: Is it possible to obtain an expression of Fisher-information, IX(Ɵ); using the m.g.f. alone, that is without requiring explicitly a probability mass function (p.m.f.) or probability density function (p.d.f.), given that the p.m.f. or p.d.f came from a one-parameter exponential family? We revisit the core of statistical inference by developing a clear link (Theorem 1.1) between the m.g.f. and IX(Ɵ). Illustrations are included.
How to Cite: Mukhopadhyay, N., 2019. Recovering Fisher-Information from the MGF Alone without Requiring Explicit PMF or PDF from a One-Parameter Exponential Family. Sri Lankan Journal of Applied Statistics, 19(1), pp.1–12. DOI: http://doi.org/10.4038/sljastats.v19i1.7984
Published on 31 Dec 2019.
Peer Reviewed

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