keyfct.grad.hz: The gradient of the hazard-rate key function

In DistanceDevelopment/mrds: Mark-Recapture Distance Sampling

The gradient of the hazard-rate key function

Description

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

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.

Value

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

DistanceDevelopment/mrds documentation built on Jan. 21, 2025, 12:33 a.m.