A Simple and Conservative Empirical Likelihood Function--Corrected


The likelihood function

L(\mu) = \left[1 +N\left((\mu-\overline{x})) / s \right)^2 \right]^{-n/2} is derived,

where \mu is the true value, \overline{x} is the mean,

and s^2 is the variance of N measurements. This form approaches a normal for n large, but can be used also for n small.

The use of this formula in data modeling is discussed.

DOI Code: 10.1285/i20705948v8n2p267

Keywords: likelihood function; empirical; data analysis; lognormal; probabilistic; Bayesian



bibitem[Miller, 2014]{Miller2014}

Miller, Guthrie (2014).

newblock A Simple and Conservative Empirical Likelihood Function.

newblock {em Electronic Journal of Applied Statistical Analysis}, 7(2), pages 344--349. (2014).


bibitem[Miller, 2015]{Miller2015}

Miller, Guthrie (2015).

newblock {em Probabilistic Interpretation of Data--A Physicist's Approach}.

newblock Lulu Publications.

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