In the statistical theory of probability distributions, the "'pseudomedian "'is the location parameter that is estimated by Hodges Lehmann statistic.
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Here, ? is a location parameter and " b " > 0, which is sometimes referred to as the diversity, is a scale parameter.
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For example, when estimating a location parameter, for a symmetric distribution a symmetric L-estimator ( such as the median or midhinge ) will be unbiased.
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The median is one of a number of ways of summarising the typical values associated with members of a statistical population; thus, it is a possible location parameter.
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In exceptional cases schools which are particularly well known with potentially long lists of notable alumni and many interlinking articles will not require the additional location parameter ( s ).
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Where \ alpha is the shape parameter, or index of stability, \ mu is the location parameter, and " c " is the scale parameter.
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Starting from these principles, Gauss demonstrates that the only law that rationalizes the choice of arithmetic mean as an estimator of the location parameter, is the normal law of errors:
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For non-symmetric populations, the Hodges-Lehmann statistic estimates the population's " pseudo-median ", a location parameter that is closely related to the median.
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He then turned the problem around by asking what form the density should have and what method of estimation should be used to get the arithmetic mean as estimate of the location parameter.
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The combination of permutation invariance and location invariance for estimating a location parameter from an independent and identically distributed dataset using a weighted average implies that the weights should be identical and sum to one.
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