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The gradient of the hazard-rate key function

Source: R/keyfct.grad.hz.R
keyfct.grad.hz.Rd

The key function contains two parameters, the scale and the shape, and so the gradient is two-dimensional. Current implementation assumes that scaled dist is x/scale, not x/width

Usage

keyfct.grad.hz(distance, key.scale, key.shape, shape = FALSE)

Arguments

distance

perpendicular distance vector

key.scale

vector of scale values

key.shape

vector of shape values

shape

is the gradient parameter the shape parameter? Defaults to FALSE

Value

matrix of derivatives of the hazard rate key function w.r.t. the scale parameter and the shape parameter.

Details

d key / d scale = (shape * exp(-(1/ (x/scale) ^ shape)) / ((x/scale) ^ shape ) * scale) d key / d shape = - ((log(x / scale) * exp(-(1/ (x/scale) ^ shape))) / (x/scale) ^ shape)

When distance = 0, the gradients are also zero. However, the equation below will result in NaN and (-)Inf due to operations such as log(0) or division by zero. We correct for this in line 33.