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# Tidy Randomly Generated Inverse Gamma Distribution Tibble

Source: `R/random-tidy-gamma-inverse.R`
`tidy_inverse_gamma.Rd`

This function will generate `n` random points from an inverse gamma distribution with a user provided, `.shape`, `.rate`, `.scale`, 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_inverse_gamma(
      .n = 50,
      .shape = 1,
      .rate = 1,
      .scale = 1/.rate,
      .num_sims = 1,
      .return_tibble = TRUE
    )

## Arguments

.n

  The number of randomly generated points you want.

.shape

  Must be strictly positive.

.rate

  An alternative way to specify the `.scale`

.scale

  Must be strictly positive.

.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 `actuar::rinvgamma()`, and its underlying `p`, `d`, and `q` functions. For more information please see `actuar::rinvgamma()`

## See also

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

Other Continuous Distribution: `tidy_beta()`, `tidy_burr()`, `tidy_cauchy()`, `tidy_chisquare()`, `tidy_exponential()`, `tidy_f()`, `tidy_gamma()`, `tidy_generalized_beta()`, `tidy_generalized_pareto()`, `tidy_geometric()`, `tidy_inverse_burr()`, `tidy_inverse_exponential()`, `tidy_inverse_normal()`, `tidy_inverse_pareto()`, `tidy_inverse_weibull()`, `tidy_logistic()`, `tidy_lognormal()`, `tidy_normal()`, `tidy_paralogistic()`, `tidy_pareto()`, `tidy_pareto1()`, `tidy_t()`, `tidy_triangular()`, `tidy_uniform()`, `tidy_weibull()`, `tidy_zero_truncated_geometric()`

Other Gamma: `tidy_gamma()`, `util_gamma_param_estimate()`, `util_gamma_stats_tbl()`

Other Inverse Distribution: `tidy_inverse_burr()`, `tidy_inverse_exponential()`, `tidy_inverse_normal()`, `tidy_inverse_pareto()`, `tidy_inverse_weibull()`

## Author

Steven P. Sanderson II, MPH

## Examples

    tidy_inverse_gamma()
    #> # A tibble: 50 × 7
    #>    sim_number     x     y     dx       dy      p     q
    #>    <fct>      <int> <dbl>  <dbl>    <dbl>  <dbl> <dbl>
    #>  1 1              1 2.55  -1.68  8.94e- 4 0.676  2.55
    #>  2 1              2 2.90   0.568 3.36e- 1 0.709  2.90
    #>  3 1              3 0.322  2.81  1.39e- 1 0.0447 0.322
    #>  4 1              4 2.54   5.06  3.37e- 2 0.675  2.54
    #>  5 1              5 1.33   7.30  1.37e- 2 0.470  1.33
    #>  6 1              6 2.18   9.55  5.38e- 3 0.632  2.18
    #>  7 1              7 0.907 11.8   9.91e- 8 0.332  0.907
    #>  8 1              8 2.77  14.0   1.27e-17 0.697  2.77
    #>  9 1              9 0.262 16.3   0        0.0218 0.262
    #> 10 1             10 0.526 18.5   0        0.150  0.526
    #> # ℹ 40 more rows