pdqr_approx_error: Diagnose pdqr approximation

Description

pdqr_approx_error() computes errors that are results of 'pdqr' approximation, which occurs because of possible tail trimming and assuming piecewise linearity of density function in case of "continuous" type. For an easy view summary, use summary().

Usage

pdqr_approx_error(f, ref_f, ..., gran = 10, remove_infinity = TRUE)

Value

A data frame with the following columns:

grid <dbl> : A grid at which errors are computed.
error <dbl> : Errors which are computed as ref_f(grid, ...) - f(grid).
abserror <dbl> : Absolute value of "error" column.

Arguments

f: A p-, d-, or q-function to diagnose. Usually the output of one of as_p(), as_d(), or as_q() default methods.
ref_f: A "true" distribution function of the same class as f. Usually the input to the aforementioned as_*() function.
...: Other arguments to ref_f. If they were supplied to as_*() function, then the exact same values must be supplied here.
gran: Degree of grid "granularity" in case of "continuous" type: number of subintervals to be produced inside every interval of density linearity. Should be not less than 1 (indicator that original column from "x_tbl" will be used, see details).
remove_infinity: Whether to remove rows corresponding to infinite error.

Details

Errors are computed as difference between "true" value (output of ref_f) and output of pdqr-function f. They are computed at "granulated" gran times grid (which is an "x" column of "x_tbl" in case f is p- or d-function and "cumprob" column if q-function). They are usually negative because of possible tail trimming of reference distribution.

Notes:

gran argument for "discrete" type is always 1.
Quantile pdqr approximation of "discrete" distribution with infinite tale(s) can result into "all one" summary of error. This is expected output and is because test grid is chosen to be quantiles of pdqr-distribution which due to renormalization can differ by one from reference ones. For example: summary(pdqr_approx_error(as_p(ppois, lambda = 10), ppois, lambda = 10)).

Examples

Run this code

d_norm <- as_d(dnorm)
error_norm <- pdqr_approx_error(d_norm, dnorm)
summary(error_norm)

# Setting `gran` results into different number of rows in output
error_norm_2 <- pdqr_approx_error(d_norm, dnorm, gran = 1)
nrow(meta_x_tbl(d_norm)) == nrow(error_norm_2)

# By default infinity errors are removed
d_beta <- as_d(dbeta, shape1 = 0.3, shape2 = 0.7)
error_beta_1 <- pdqr_approx_error(d_beta, dbeta, shape1 = 0.3, shape2 = 0.7)
summary(error_beta_1)

# To not remove them, set `remove_infinity` to `FALSE`
error_beta_2 <- pdqr_approx_error(
  d_beta, dbeta, shape1 = 0.3, shape2 = 0.7, remove_infinity = FALSE
)
summary(error_beta_2)