Zulfia Estimation Theory (ZET): (f (x|θ) is imposed in 1922. Generated in 2026)

Abstract

AbstractSince Fisher introduced Maximum Likelihood Estimation in 1922, statisticalinference has imposed a distributional assumption f (x|θ) before examining a singleobservation. For 104 years this imposition has been treated as necessary. It is not.This paper introduces Zulfia Estimation Theory (ZET): estimation withoutimposed distributions. The estimator is not the parameter that maximises an imposedlikelihood. It is the parameter that closes the Zulfia Gap:ˆθZET : ∆(θ, x) = 0where ∆(θ, x) = x − MZ [θ] is the Zulfia Deviation — generated by the data, neverimposed. We prove that MLE is a special case of ZET when the imposed distributionaccidentally matches the generated deviation structure. ZET is always structurallycorrect. MLE is correct only when its assumption is correct. The confusion of 104years ends here