Weibull distribution functions

Usage

iweibull(x, shape, scale = 1)

mweibull(x, shape, scale = 1)

parameters_weibull(...)

Arguments

x: A numeric vector
shape: Shape parameter for Weibull distribution. See stats::dweibull().
scale: Scale parameter for Weibull distribution. See stats::dweibull().
...: currently ignored

Value

A numeric vector

Details

Intensity function for the Weibull distribution. $$ iweibull(x) = \left( \frac{shape}{scale} \right) \cdot \left( \frac{x}{scale} \right)^{shape - 1} $$

Mean intensity function for the Weibull distribution. $$ mweibull(x) = \left( \frac{x}{scale} \right)^{shape} $$

parameters_weibull() returns a list() with two components: shape and scale, each of which is a list() of distribution parameters. These parameters are used to define the prior distributions for the hyperparameters.

Examples

# Compute the intensities and plot them
iweibull(1, shape = 1, scale = 1)
#> [1] 1
plot(x = 1:10, y = iweibull(1:10, shape = 2, scale = 2))


# Compute various values of the distribution
mweibull(1, shape = 1, scale = 1)
#> [1] 1
plot(x = 1:10, y = mweibull(1:10, shape = 1, scale = 1))

plot(x = 1:10, y = mweibull(1:10, shape = 1, scale = 2))

plot(x = 1:10, y = mweibull(1:10, shape = 0.5, scale = 2))

plot(x = 1:10, y = mweibull(1:10, shape = 0.5, scale = 100))

plot(x = 1:10, y = mweibull(1:10, shape = 2, scale = 2))

plot(x = 1:10, y = mweibull(1:10, shape = 2, scale = 100))


# Generate prior distribution hyperparameters
parameters_weibull()
#> $shape
#> $shape$dist
#> [1] "gamma"
#> 
#> $shape$shape
#> [1] 1
#> 
#> $shape$rate
#> [1] 2
#> 
#> $shape$initial_value
#> [1] 0.1
#> 
#> $shape$lower_bound
#> [1] 1e-04
#> 
#> $shape$upper_bound
#> [1] 10
#> 
#> 
#> $scale
#> $scale$dist
#> [1] "gamma"
#> 
#> $scale$shape
#> [1] 3
#> 
#> $scale$rate
#> [1] 1.2
#> 
#> $scale$initial_value
#> [1] 0.5
#> 
#> $scale$lower_bound
#> [1] 1e-08
#> 
#> $scale$upper_bound
#> [1] 1e+05
#> 
#>