Kernel Density Estimator 1.0

% Reliable and extremely fast kernel density estimator for one-dimensional data;% Gaussian kernel is assumed and the bandwidth is chosen automatically;% Unlike many other implementations, this one is immune to problems% caused by multimodal densities with widely separated modes (see example). The% estimation does not deteriorate for multimodal densities, because we never assume% a parametric model for the data.% INPUTS:% data - a vector of data from which the density estimate is constructed;% n - the number of mesh points used in the uniform discretization of the% interval [MIN, MAX]; n has to be a power of two; if n is not a power of two, then% n is rounded up to the next power of two, i.e., n is set to n=2^ceil(log2(n));% the default value of n is n=2^12;% MIN, MAX - defines the interval [MIN,MAX] on which the density estimate is constructed;% the default values of MIN and MAX are:% MIN=min(data)-Range/10 and MAX=max(data)+Range/10, where Range=max(data)-min(data);% OUTPUTS:% bandwidth - the optimal bandwidth (Gaussian kernel assumed);% density - column vector of length 'n' with the values of the density% estimate at the grid points;% xmesh - the grid over which the density estimate is computed;% - If no output is requested, then the code automatically plots a graph of% the density estimate.% cdf - column vector of length 'n' with the values of the cdf% Reference:% Kernel density estimation via diffusion% Z. I. Botev, J. F. Grotowski, and D. P. Kroese (2010)% Annals of Statistics, Volume 38, Number 5, pages 2916-2957.%% Example:% data=[randn(100,1);randn(100,1)*2+35 ;randn(100,1)+55];% kde(data,2^14,min(data)-5,max(data)+5);% Notes: If you have a more reliable and accurate one-dimensional kernel density% estimation software, please email me at botev@maths.uq.edu.a

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	039n039,  Column,  Computed,  Graph,  Length,  Optimal,  Output,  Plots,  Requested,  Xmesh
Users rating:	0/10