Piecewise Linear Distribution
Overview
The piecewise linear distribution creates a nonparametric representation of the cumulative distribution function (cdf) by linearly connecting the known cdf values from the sample data.
Parameters
The piecewise linear distribution uses the following parameters.
Parameter | Description |
---|---|
x | Vector of x values at which the cdf changes slope |
Fx | Vector of cdf values that correspond to each value in
x |
Cumulative Distribution Function
The piecewise linear distribution constructs a continuous cumulative distribution
function (cdf) by connecting the empirical cdf values such that the cdf increases
linearly between x
(j) and
x
(j + 1).
Relationship to Other Distributions
The piecewise linear distribution is a continuous version of the discrete empirical cumulative distribution function (ecdf).