Diagnose pdqr approximation

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().

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

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.

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.

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)).

See also

enpoint() for representing pdqr-function as a set of points with desirable number of rows.

Examples

d_norm <- as_d(dnorm)
error_norm <- pdqr_approx_error(d_norm, dnorm)
summary(error_norm)
#>       grid            error               abserror        
#>  Min.   :-4.753   Min.   :-7.979e-07   Min.   :9.900e-12  
#>  1st Qu.:-2.377   1st Qu.:-4.000e-07   1st Qu.:1.975e-09  
#>  Median : 0.000   Median :-5.552e-08   Median :5.552e-08  
#>  Mean   : 0.000   Mean   :-2.104e-07   Mean   :2.104e-07  
#>  3rd Qu.: 2.377   3rd Qu.:-1.975e-09   3rd Qu.:4.000e-07  
#>  Max.   : 4.753   Max.   :-9.900e-12   Max.   :7.979e-07  

# 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)
#> [1] TRUE

# 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)
#>       grid             error             abserror       
#>  Min.   :0.00001   Min.   :-13.9547   Min.   :  0.0167  
#>  1st Qu.:0.25000   1st Qu.: -0.0278   1st Qu.:  0.0174  
#>  Median :0.50000   Median : -0.0199   Median :  0.0199  
#>  Mean   :0.50000   Mean   : -0.0215   Mean   :  0.0470  
#>  3rd Qu.:0.74999   3rd Qu.: -0.0174   3rd Qu.:  0.0278  
#>  Max.   :0.99999   Max.   :587.9396   Max.   :587.9396  

# 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)
#>       grid          error              abserror      
#>  Min.   :0.00   Min.   :-13.95467   Min.   :0.01671  
#>  1st Qu.:0.25   1st Qu.: -0.02783   1st Qu.:0.01736  
#>  Median :0.50   Median : -0.01987   Median :0.01987  
#>  Mean   :0.50   Mean   :      Inf   Mean   :    Inf  
#>  3rd Qu.:0.75   3rd Qu.: -0.01736   3rd Qu.:0.02784  
#>  Max.   :1.00   Max.   :      Inf   Max.   :    Inf