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# Tidy Randomly Generated Paralogistic Distribution Tibble

Source: `R/random-tidy-paralogistic.R`
`tidy_paralogistic.Rd`

This function will generate `n` random points from a paralogistic 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_paralogistic(
      .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::rparalogis()`, and its underlying `p`, `d`, and `q` functions. For more information please see `actuar::rparalogis()`

## See also

https://en.wikipedia.org/wiki/Logistic_distribution

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_gamma()`, `tidy_inverse_normal()`, `tidy_inverse_pareto()`, `tidy_inverse_weibull()`, `tidy_logistic()`, `tidy_lognormal()`, `tidy_normal()`, `tidy_pareto()`, `tidy_pareto1()`, `tidy_t()`, `tidy_triangular()`, `tidy_uniform()`, `tidy_weibull()`, `tidy_zero_truncated_geometric()`

Other Logistic: `tidy_logistic()`, `util_logistic_param_estimate()`, `util_logistic_stats_tbl()`

## Author

Steven P. Sanderson II, MPH

## Examples

    tidy_paralogistic()
    #> # A tibble: 50 × 7
    #>    sim_number     x      y    dx       dy     p      q
    #>    <fct>      <int>  <dbl> <dbl>    <dbl> <dbl>  <dbl>
    #>  1 1              1  0.788 -2.74 1.02e- 3 0.441  0.788
    #>  2 1              2  0.419  1.36 2.13e- 1 0.296  0.419
    #>  3 1              3  2.61   5.45 2.18e- 2 0.723  2.61
    #>  4 1              4  1.77   9.55 1.19e- 2 0.638  1.77
    #>  5 1              5  0.264 13.6  6.42e- 6 0.209  0.264
    #>  6 1              6 81.0   17.7  2.60e-17 0.988 81.0
    #>  7 1              7  0.514 21.8  0        0.339  0.514
    #>  8 1              8  0.516 25.9  4.16e-18 0.340  0.516
    #>  9 1              9  0.933 30.0  0        0.483  0.933
    #> 10 1             10  0.186 34.1  3.51e-16 0.157  0.186
    #> # ℹ 40 more rows