Hazard rate key function

This function provides the hazard rate key function for model fitting in distance sampling.

Usage

hazard_rate_key(x, sigma, beta)

Arguments

x

vector of perpendicular distances from the transect.

sigma

scale parameter.

beta

shape parameter.

Value

A numeric value corresponding to a given value of x, sigma and beta.

Details

This is the hazard rate key function with parameters sigma and beta. Its expression is given by

\(g(x) = 1 - \exp((\frac{-x}{\sigma})^{-\beta},\)

for x > 0.

See also

Other key functions: half_norm_key(), uniform_key()

Author

Jaime Mosquera Gutiérrez, jmosquerag@unal.edu.co

Examples

library(EstimationTools)

#----------------------------------------------------------------------------
# Example: Hazard rate function
hazard_rate_key(x=1, sigma=2, beta=3)
#> [1] 0.9996645
curve(hazard_rate_key(x, sigma=2, beta=3), from=0, to=10, ylab='g(x)')


#----------------------------------------------------------------------------