scores_t: Calculating scores for Student's t-distribution

In scoringRules: Scoring Rules for Parametric and Simulated Distribution Forecasts

Calculating scores for Student's t-distribution

Description

These functions calculate scores (CRPS, logarithmic score) and their gradient and Hessian with respect to the parameters of a location-scale transformed Student's t-distribution. Furthermore, the censoring transformation and the truncation transformation may be introduced on top of the location-scale transformed t-distribution.

Usage

## score functions
crps_t(y, df, location = 0, scale = 1)
crps_ct(y, df, location = 0, scale = 1, lower = -Inf, upper = Inf)
crps_tt(y, df, location = 0, scale = 1, lower = -Inf, upper = Inf)
crps_gtct(y, df, location = 0, scale = 1, lower = -Inf, upper = Inf, lmass = 0, umass = 0)
logs_t(y, df, location = 0, scale = 1)
logs_tt(y, df, location = 0, scale = 1, lower = -Inf, upper = Inf)
dss_t(y, df, location = 0, scale = 1)

## gradient (location, scale) functions
gradcrps_t(y, df, location = 0, scale = 1)
gradcrps_ct(y, df, location = 0, scale = 1, lower = -Inf, upper = Inf)
gradcrps_tt(y, df, location = 0, scale = 1, lower = -Inf, upper = Inf)

## Hessian (location, scale) functions
hesscrps_t(y, df, location = 0, scale = 1)
hesscrps_ct(y, df, location = 0, scale = 1, lower = -Inf, upper = Inf)
hesscrps_tt(y, df, location = 0, scale = 1, lower = -Inf, upper = Inf)

Arguments

y	vector of observations.
df	vector of degrees of freedom.
location	vector of location parameters.
scale	vector of scale paramters.
lower, upper	lower and upper truncation/censoring bounds.
lmass, umass	vectors of point masses in lower and upper respectively.

Value

For the CRPS functions: a vector of score values.

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

scoringRules documentation built on Sept. 18, 2024, 5:09 p.m.