dist_shash

Usage

dist_shash(mu, sigma, eps = 0, delta = 1)

dist_conditioned(marginal, m, s)

Reference models return predictive distributions as distributional vectors, so cdf(), quantile(), density(), generate(), mean(), variance(), hilo(), tibble columns, and ggdist layers all work. Gaussian fits use distributional::dist_normal(); SHASH fits use dist_shash(); uncertainty = "total" predictions from location-scale and SHASH fits are equal-weight mixtures over coefficient draws (an internal dist_shash_draws class, one SHASH parameter set per draw and observation); history-conditioned forecasts are dist_conditioned(); a spec with a response transform returns the push-forward of the fitted distribution onto the response scale (an internal dist_warped class).

Arguments

Argument	Description
mu, sigma, eps, delta	Location, scale (> 0), skewness, and tail weight (> 0), recycled to a common length.
marginal	A distribution vector of marginal predictive distributions.
m, s	Conditional mean and standard deviation (> 0) of the latent normal score, recycled to length(marginal).

Details

dist_shash() follows the mgcv::shash() parameterisation. With $z = (y-\mu)/(\sigma\delta)$, $F(y) = \Phi(\sinh(\delta,\mathrm{asinh}(z)-\epsilon))$; eps = 0, delta = 1 is the Gaussian $N(\mu, \sigma^2)$.

dist_conditioned() maps a marginal predictive distribution through a conditional normal score: $F_*(y) = \Phi((z(y)-m)/s)$ with $z(y) = \Phi^{-1}(F(y))$, so m = 0, s = 1 recovers the marginal.

Tail probabilities of every class are evaluated in log space, so scores for observations 40 standard deviations out remain finite and distinct (see as_scores()).

Value

A distributional distribution vector.

Examples

d <- dist_shash(mu = 0.2, sigma = 1.1, eps = 0.3, delta = 0.9)
d

<distribution[1]>
[1] SHASH(0.2, 1.1, 0.3, 0.9)

cdf(d, 1.5)

[1] 0.7675768

quantile(d, c(0.05, 0.5, 0.95))

[[1]]
[1] -1.0904537  0.5361452  2.9544300

mean(d)

[1] 0.6872512

as_scores(d, c(-2, 0, 2))

# A tibble: 3 × 8
  observed median centile      z tail_prob tail_surprisal residual log_density
     <dbl>  <dbl>   <dbl>  <dbl>     <dbl>          <dbl>    <dbl>       <dbl>
1       -2  0.536 0.00462 -2.60    0.00923          4.69    -2.54        -4.27
2        0  0.536 0.309   -0.499   0.618            0.482   -0.536       -1.05
3        2  0.536 0.855    1.06    0.289            1.24     1.46        -1.93

dist_conditioned(d, m = 0.4, s = 0.7)

<distribution[1]>
[1] SHASH(0.2, 1.1, 0.3, 0.9) | N(0.4, 0.7)