Change center and spread of distribution — form

These functions implement linear transformations, output distribution of which has desired center and spread. These functions are useful for creating distributions with some input center and spread value based on present distribution, which is a common task during hypothesis testing.

form_recenter(f, to, method = "mean")

form_respread(f, to, method = "sd", center_method = "mean")

Arguments

f	A pdqr-function.
to	A desired value of summary.
method	Method of computing center for `form_recenter()` and spread for `form_respread()`. Values should be one of possible `method` values from `summ_center()` and `summ_spread()` respectively.
center_method	Method of computing center for `form_respread()` in order to preserve it in output.

Value

A pdqr-function describing distribution with desired center or spread.

Details

form_recenter(f, to, method) is basically a f - summ_center(f, method) + to: it moves distribution without affecting its shape so that output distribution has center at to.

form_respread(f, to, method, center_method) is a following linear transformation: coef * (f - center) + center, where center is summ_center(f, center_method) and coef is computed so as to guarantee output distribution to have spread equal to to. In other words, this linear transformation stretches distribution around its center until the result has spread equal to to (center remains the same as in input f).

Examples

my_beta <- as_d(dbeta, shape1 = 1, shape2 = 3)

my_beta2 <- form_recenter(my_beta, to = 2)
summ_center(my_beta2)
#> [1] 2

my_beta3 <- form_respread(my_beta2, to = 10, method = "range")
summ_spread(my_beta3, method = "range")
#> [1] 10
## Center remains unchainged
summ_center(my_beta3)
#> [1] 2