scores_norm | R Documentation |
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.
## 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)
y |
vector of observations. |
mean |
an alternative way to specify |
sd |
an alternative way to specify |
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 |
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.
## Not run:
# 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
## End(Not run)
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