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The weighted likelihood bootstrap replaces integer repeat numbers for data points in the usual resampling bootstrap, with continuous values. This distribution is the same if read from lower to higher values or higher to lower values. The point indices of the weights are placed so the the distribution of weights runs from 0.5 to n+0.5, similar to creating a bar graph of the weight distribution with the ith bar extending from i-0.5 to i+0.5, and then the cumulative distribution is the integral of this, and discrete values are read off at integer points. The use of interpolation may give slightly different results from methods not using interpolation. Interpolation is used to avoid the existence of upper and lower weighted medians and instead give a consistent result (see ). Wtmedian(x,sd) % gives median only, no bootstrapĬnt=10000 =wtmedian(x,sd,cnt) % additional bootstrap samples =wtmedian(x) % no (or unit) sds: usual median If standard deviation of median is required, a weighted likelihood bootstrap calculates the mean and if required an empirical distribution of the median is returned.

The point indexes of the weights are placed symmetrically and interpolation for the 50% point, is used to give consistent results.

S std (A,w,dim) returns the standard deviation along dimension dim for any of the previous syntaxes. This syntax is valid for MATLAB versions R2018b and later. If standard deviations not given normal mean is calculated. S std (A,w,'all') computes the standard deviation over all elements of A when w is either 0 or 1. Input is data and standard deviations of data points.

Calculates weighted median using interpolation and optionally estimates standard deviation and distribution of median.