Access a distribution's quantiles.
Usage
eval_quantile(distribution, at)
enframe_quantile(..., at, arg_name = ".arg", fn_prefix = "quantile", sep = "_")Arguments
- distribution, ...
A distribution, or possibly multiple distributions in the case of
....- at
Vector of values to evaluate the representation at.
- arg_name
For
enframe_, name of the column containing the function arguments. Length 1 character vector.- fn_prefix
For
enframe_, name of the function to appear in the column(s). Length 1 character vector.- sep
When
enframe'ing more than one distribution, the character that will be separating thefn_nameand the distribution name. Length 1 character vector.
Value
The evaluated representation in vector form (for eval_)
with length matching the length of at, and data frame
or tibble form (for enframe_) with number of rows matching the
length of at. The at input occupies the first column,
named .arg by default, or the specification in arg_name;
the evaluated representations for each distribution in ...
go in the subsequent columns (one column per distribution). For a
single distribution, this column is named according to the
representation by default (cdf, survival, quantile, etc.),
or the value in fn_prefix. For multiple distributions, unnamed
distributions are auto-named, and columns are named
<fn_prefix><sep><distribution_name> (e.g., cdf_distribution1).
Details
The 0- and 1-quantiles are the ends of the distribution's support: the
0-quantile is its lower end and the 1-quantile its upper end. They are
read from the support (see support()) rather than computed, so an
unbounded distribution gives -Inf and Inf instead of a large finite
number found by searching into the tail.
When a quantile function does not exist, the remaining probabilities are found by inverting the CDF by bisection: an interval known to contain the solution is progressively cut in half, moving into whichever half still contains it. The whole vector is solved together — one vectorized CDF evaluation per step rather than one per probability — so evaluating many quantiles at once is considerably faster than one at a time. Because the support says where the atoms (discrete mass points) are, a probability landing inside an atom's jump in the CDF is returned as that atom exactly, rather than approximately. Tolerance is roughly 1e-9 in the quantile value, unless the maximum number of iterations (200) is reached.
See also
Other distributional representations:
eval_cdf(),
eval_chf(),
eval_density(),
eval_hazard(),
eval_odds(),
eval_pmf(),
eval_return(),
eval_survival()
Examples
d <- dst_unif(0, 4)
eval_quantile(d, at = 1:9 / 10)
#> [1] 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6
enframe_quantile(d, at = 1:9 / 10)
#> # A tibble: 9 × 2
#> .arg quantile
#> <dbl> <dbl>
#> 1 0.1 0.4
#> 2 0.2 0.8
#> 3 0.3 1.2
#> 4 0.4 1.6
#> 5 0.5 2
#> 6 0.6 2.4
#> 7 0.7 2.8
#> 8 0.8 3.2
#> 9 0.9 3.6