Compute for pair of pdqr-functions the optimal threshold that separates distributions they represent. In other words, summ_separation() solves a binary classification problem with one-dimensional linear classifier: values not more than some threshold are classified as one class, and more than threshold - as another. Order of input functions doesn't matter.

summ_separation(f, g, method = "KS", n_grid = 10001)

Arguments

f

A pdqr-function of any type and class. Represents "true" distribution of "negative" values.

g

A pdqr-function of any type and class. Represents "true" distribution of "positive" values.

method

Separation method. Should be one of "KS" (Kolmogorov-Smirnov), "GM", "OP", "F1", "MCC" (all four are methods for computing classification metric in summ_classmetric()).

n_grid

Number of grid points to be used during optimization.

Value

A single number representing optimal separation threshold.

Details

All methods:

  • Return middle point of nearest support edges in case of non-overlapping or "touching" supports of f and g.

  • Return the smallest optimal solution in case of several candidates.

Method "KS" computes "x" value at which corresponding p-functions of f and g achieve supremum of their absolute difference (so input order of f and g doesn't matter). If input pdqr-functions have the same type, then result is a point of maximum absolute difference. If inputs have different types, then absolute difference of p-functions at the result point can be not the biggest. In that case output represents a left limit of points at which target supremum is reached (see Examples).

Methods "GM", "OP", "F1", "MCC" compute threshold which maximizes corresponding classification metric for best suited classification setup. They evaluate metrics at equidistant grid (with n_grid elements) for both directions (summ_classmetric(f, g, *) and summ_classmetric(g, f, *)) and return threshold which results into maximum of both setups. Note that other summ_classmetric() methods are either useless here (always return one of the edges) or are equivalent to ones already present.

See also

summ_roc() for computing ROC curve related summaries.

summ_classmetric() for computing of classification metric for ordered classification setup.

Other summary functions: summ_center, summ_classmetric, summ_distance, summ_entropy, summ_hdr, summ_interval, summ_moment, summ_order, summ_prob_true, summ_pval, summ_quantile, summ_roc, summ_spread

Examples

d_norm_1 <- as_d(dnorm) d_unif <- as_d(dunif) summ_separation(d_norm_1, d_unif, method = "KS")
#> [1] 0
summ_separation(d_norm_1, d_unif, method = "OP")
#> [1] 0.3593589
# Mixed types for "KS" method p_dis <- new_p(1, "discrete") p_unif <- as_p(punif) thres <- summ_separation(p_dis, p_unif) abs(p_dis(thres) - p_unif(thres))
#> [1] 0
# Actual difference at `thres` is 0. However, supremum (equal to 1) as # limit value is # reached there. x_grid <- seq(0, 1, by = 1e-3) plot(x_grid, abs(p_dis(x_grid) - p_unif(x_grid)), type = "b")
# Handling of non-overlapping supports summ_separation(new_d(2, "discrete"), new_d(3, "discrete"))
#> [1] 2.5
# The smallest "x" value is returned in case of several optimal thresholds summ_separation(d_norm_1, d_norm_1) == meta_support(d_norm_1)[1]
#> [1] TRUE