Kdensity

Purpose

Calculates the kernel density estimate.

Synopsis

[kde, newx] = kdensity(x,code,width,n,at)

Description

Produces the kernel density estimate of the data contained in the input vector (x) which must be real.

Inputs

• x = The name of a matrix (column vector) in which the sample data is stored.
• code = Integer between 1 and 7 indicating which kernel to use.

1 - Bivwight

2 - Cosine

3 - Epanechnikov {default}

4 - Gaussian

5 - Parzen

6 - Triangle

• width = scalar, optional window width to use in the kernel calculation. If not specified, then the optimal window width is used according to the calculation:

$min\left\{{\sigma }_{x},{\frac {p_{75}-p_{25}}{1.349}}\right\}\left({\frac {0.9}{n}}\right)^{0.20}$

• n = scalar, number of points at which to estimate the density.
• at = vector, allows the user to specify a vector of points at which the density should be estimated. By using this option, it makes it easier to overlay density estimates for different samples on the same graph.

Outputs

• newx = x input returned.
• kde = The return value is a structure with fields:
  • x = vector of points where density was estimated. Will be the same as 'at' input if used.
  • fx = ?
  • n = number of points at which to estimate density. Same as 'n' input if used.
  • width = window width used. Same as 'width' input if used.
  • kernel = name of kernel used.

Examples

 kde = kdensity(x,2);
 kde = kdensity(x,2,22.4);
 kde = kdensity(x,2,22.4,50);
 kde = kdensity(x,2,22.4,50,y);

See Also

plotkd