Mathematical Statistics

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5 domain-specific abstractions whose origin domain is Mathematical Statistics.

• Energy distance — A metric between probability distributions built from expected pairwise Euclidean distances within and across independent samples.
• K-statistic — A symmetric unbiased estimator of a population cumulant constructed from sample power sums.
• Monotone Likelihood Ratio Property — Order a parametric family so every higher-parameter to lower-parameter likelihood ratio is nondecreasing in one statistic, making larger statistics monotonically stronger evidence for the higher parameter.
• Noncentral distribution — A distribution family for a statistic under a shifted alternative, indexed by a noncentrality parameter in addition to the central family parameters.
• Polykay — Estimate a specified product of population cumulants without finite-sample bias by evaluating its partition-indexed symmetric polynomial on an i.i.d. sample.