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# Tidy Randomly Generated Negative Binomial Distribution Tibble

Source: `R/random-tidy-negative-binomial.R`
`tidy_negative_binomial.Rd`

This function will generate `n` random points from a negative binomial distribution with a user provided, `.size`, `.prob`, and number of random simulations to be produced. The function returns a tibble with the simulation number column the x column which corresponds to the n randomly generated points, the `d_`, `p_` and `q_` data points as well.

The data is returned un-grouped.

The columns that are output are:

- `sim_number` The current simulation number.

- `x` The current value of `n` for the current simulation.

- `y` The randomly generated data point.

- `dx` The `x` value from the `stats::density()` function.

- `dy` The `y` value from the `stats::density()` function.

- `p` The values from the resulting p_ function of the distribution family.

- `q` The values from the resulting q_ function of the distribution family.

## Usage

    tidy_negative_binomial(
      .n = 50,
      .size = 1,
      .prob = 0.1,
      .num_sims = 1,
      .return_tibble = TRUE
    )

## Arguments

.n

  The number of randomly generated points you want.

.size

  target for number of successful trials, or dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer.

.prob

  Probability of success on each trial where 0 < .prob <= 1.

.num_sims

  The number of randomly generated simulations you want.

.return_tibble

  A logical value indicating whether to return the result as a tibble. Default is TRUE.

## Value

A tibble of randomly generated data.

## Details

This function uses the underlying `stats::rnbinom()`, and its underlying `p`, `d`, and `q` functions. For more information please see `stats::rnbinom()`

## See also

https://openacttexts.github.io/Loss-Data-Analytics/ChapSummaryDistributions.html

Other Discrete Distribution: `tidy_bernoulli()`, `tidy_binomial()`, `tidy_hypergeometric()`, `tidy_poisson()`, `tidy_zero_truncated_binomial()`, `tidy_zero_truncated_negative_binomial()`, `tidy_zero_truncated_poisson()`

Other Binomial: `tidy_binomial()`, `tidy_zero_truncated_binomial()`, `tidy_zero_truncated_negative_binomial()`, `util_binomial_param_estimate()`, `util_binomial_stats_tbl()`, `util_negative_binomial_param_estimate()`

## Author

Steven P. Sanderson II, MPH

## Examples

    tidy_negative_binomial()
    #> # A tibble: 50 × 7
    #>    sim_number     x     y     dx       dy     p     q
    #>    <fct>      <int> <int>  <dbl>    <dbl> <dbl> <dbl>
    #>  1 1              1    15 -9.21  0.000272 0.815    15
    #>  2 1              2     0 -8.14  0.000754 0.1       0
    #>  3 1              3    11 -7.07  0.00187  0.718    11
    #>  4 1              4     1 -6.00  0.00412  0.190     1
    #>  5 1              5     8 -4.93  0.00815  0.613     8
    #>  6 1              6    18 -3.86  0.0145   0.865    18
    #>  7 1              7     0 -2.79  0.0231   0.1       0
    #>  8 1              8     0 -1.72  0.0334   0.1       0
    #>  9 1              9     5 -0.655 0.0438   0.469     5
    #> 10 1             10     5  0.415 0.0527   0.469     5
    #> # ℹ 40 more rows