scoringRules (version 1.1.3)

scores_norm: Calculating scores for the normal distribution

Description

These functions calculate scores (CRPS, LogS, DSS) and their gradient and Hessian with respect to the parameters of a location-scale transformed normal distribution. Furthermore, the censoring transformation and the truncation transformation may be introduced on top of the location-scale transformed normal distribution.

Usage

## score functions
crps_norm(y, mean = 0, sd = 1, location = mean, scale = sd)
crps_cnorm(y, location = 0, scale = 1, lower = -Inf, upper = Inf)
crps_tnorm(y, location = 0, scale = 1, lower = -Inf, upper = Inf)
crps_gtcnorm(y, location = 0, scale = 1, lower = -Inf, upper = Inf, lmass = 0, umass = 0)
logs_norm(y, mean = 0, sd = 1, location = mean, scale = sd)
logs_tnorm(y, location = 0, scale = 1, lower = -Inf, upper = Inf)
dss_norm(y, mean = 0, sd = 1, location = mean, scale = sd)
## gradient (location, scale) functions
gradcrps_norm(y, location = 0, scale = 1)
gradcrps_cnorm(y, location = 0, scale = 1, lower = -Inf, upper = Inf)
gradcrps_tnorm(y, location = 0, scale = 1, lower = -Inf, upper = Inf)
## Hessian (location, scale) functions
hesscrps_norm(y, location = 0, scale = 1)
hesscrps_cnorm(y, location = 0, scale = 1, lower = -Inf, upper = Inf)
hesscrps_tnorm(y, location = 0, scale = 1, lower = -Inf, upper = Inf)

Value

For the score functions: a vector of score values.

For the gradient and Hessian functions: a matrix with column names corresponding to the respective partial derivatives.

Arguments

y

vector of observations.

mean

an alternative way to specify location.

sd

an alternative way to specify scale.

location

vector of location parameters.

scale

vector of scale parameters.

lower, upper

lower and upper truncation/censoring bounds.

lmass, umass

vectors of point masses in lower and upper respectively.

Examples

if (FALSE) {
# Illustrations: Compare CRPS of analytical distribution to 
# CRPS of a large sample drawn from this distribution 
# (expect scores to be similar)

# First illustration: Standard normal 
# Consider CRPS at arbitrary evaluation point (value of outcome)
y <- 0.3
crps_norm(y = y) # score of analytical dist.
# draw standard normal sample of size 10000
dat <- rnorm(1e4)
crps_sample(y = y, dat = dat) # score of sample

# Second illustration: Truncated standard normal
# truncation point
upper <- 1
crps_tnorm(y = y, upper = upper) # score of analytical dist.
# sample from truncated normal 
dat_trunc <- dat[dat <= upper] 
crps_sample(y = y, dat = dat_trunc) # score of sample

# Third illustration: Censored standard normal (censoring at \code{upper})
crps_cnorm(y = y, upper = upper) # score of analytical dist.
# sample from censored normal 
dat_cens <- ifelse(dat <= upper, dat, upper)
crps_sample(y = y, dat = dat_cens) # score of sample
}