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 |

A pdqr-function of the same class and
type (if not forced otherwise in `args_new`

) as `f`

.

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
# \donttest{
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)#> Probability mass function of discrete type
#> Support: [1.8, 4] (23 elements) # To change type of output, supply it in `args_new`
form_estimate(
d_dis, stat = mean, sample_size = 10,
args_new = list(type = "continuous")
)#> Density function of continuous type
#> Support: ~[1.67226, 4.12774] (511 intervals)
# 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))
# 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)#> Probability mass function of discrete type
#> Support: [0, 1] (2 elements, probability of 1: 0.0318)# }
```