Create a pdqr-function for distribution of sample estimate
Based on pdqr-function, statistic function, and sample size describe the distribution of sample estimate. This might be useful for statistical inference.
form_estimate(f, stat, sample_size, ..., n_sample = 10000, args_new = list())
f |
A pdqr-function. |
stat |
Statistic function. Should be able to accept numeric vector of
size |
sample_size |
Size of sample for which distribution of sample estimate is needed. |
... |
Other arguments for |
n_sample |
Number of elements to generate from distribution of sample estimate. |
args_new |
List of extra arguments for new_*() function to
control |
General idea is to create a sample from target distribution by
generating n_sample samples of size sample_size and compute for each of
them its estimate by calling input stat function. If created sample is
logical, boolean pdqr-function (type "discrete" with elements being
exactly 0 and 1) is created with probability of being true estimated as share
of TRUE values (after removing possible NA). If sample is numeric, it is
used as input to new_*() of appropriate class with type equal to type of
f (if not forced otherwise in args_new).
Notes:
This function may be very time consuming for large values of n_sample and
sample_size, as total of n_sample*sample_size numbers are generated and
stat function is called n_sample times.
Output distribution might have a bias compared to true distribution of
sample estimate. One useful technique for bias correction: compute mean value
of estimate using big sample_size (with mean(as_r(f)(sample_size))) and
then recenter distribution to actually have that as a mean.
Other form functions:
form_mix(),
form_regrid(),
form_resupport(),
form_retype(),
form_smooth(),
form_tails(),
form_trans()
# These examples take some time to run, so be cautious
set.seed(101)
# Type "discrete"
d_dis <- new_d(data.frame(x = 1:4, prob = 1:4 / 10), "discrete")
## Estimate of distribution of mean
form_estimate(d_dis, stat = mean, sample_size = 10)
## To change type of output, supply it in `args_new`
form_estimate(
d_dis, stat = mean, sample_size = 10,
args_new = list(type = "continuous")
)
# Type "continuous"
d_unif <- as_d(dunif)
## Supply extra named arguments for `stat` in `...`
plot(form_estimate(d_unif, stat = mean, sample_size = 10, trim = 0.1))
lines(
form_estimate(d_unif, stat = mean, sample_size = 10, trim = 0.3),
col = "red"
)
lines(
form_estimate(d_unif, stat = median, sample_size = 10),
col = "blue"
)
# Statistic can return single logical value
d_norm <- as_d(dnorm)
all_positive <- function(x) {
all(x > 0)
}
## Probability of being true should be around 0.5^5
form_estimate(d_norm, stat = all_positive, sample_size = 5)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.