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# Estimate Negative Binomial Parameters

Source: `R/est-param-negative-binomial.R`
`util_negative_binomial_param_estimate.Rd`

The function will return a list output by default, and if the parameter `.auto_gen_empirical` is set to `TRUE` then the empirical data given to the parameter `.x` will be run through the `tidy_empirical()` function and combined with the estimated negative binomial data.

Two different methods of shape parameters are supplied:

- MLE/MME

- MMUE

## Usage

    util_negative_binomial_param_estimate(.x, .size, .auto_gen_empirical = TRUE)

## Arguments

.x

  The vector of data to be passed to the function.

.size

  The size parameter.

.auto_gen_empirical

  This is a boolean value of TRUE/FALSE with default set to TRUE. This will automatically create the `tidy_empirical()` output for the `.x` parameter and use the `tidy_combine_distributions()`. The user can then plot out the data using `$combined_data_tbl` from the function output.

## Value

A tibble/list

## Details

This function will attempt to estimate the negative binomial size and prob parameters given some vector of values.

## See also

Other Parameter Estimation: `util_bernoulli_param_estimate()`, `util_beta_param_estimate()`, `util_binomial_param_estimate()`, `util_burr_param_estimate()`, `util_cauchy_param_estimate()`, `util_exponential_param_estimate()`, `util_gamma_param_estimate()`, `util_geometric_param_estimate()`, `util_hypergeometric_param_estimate()`, `util_logistic_param_estimate()`, `util_lognormal_param_estimate()`, `util_normal_param_estimate()`, `util_pareto_param_estimate()`, `util_poisson_param_estimate()`, `util_triangular_param_estimate()`, `util_uniform_param_estimate()`, `util_weibull_param_estimate()`

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

## Author

Steven P. Sanderson II, MPH

## Examples

    library(dplyr)
    library(ggplot2)

    x <- as.integer(mtcars$mpg)
    output <- util_negative_binomial_param_estimate(x, .size = 1)

    output$parameter_tbl
    #> # A tibble: 2 × 9
    #>   dist_type         samp_size   min   max  mean method   size   prob shape_ratio
    #>   <chr>                 <int> <dbl> <dbl> <dbl> <chr>   <dbl>  <dbl>       <dbl>
    #> 1 Negative Binomial        32    10    33  19.7 EnvSta…    32 0.0483        662
    #> 2 Negative Binomial        32    10    33  19.7 EnvSta…    32 0.0469        682.

    output$combined_data_tbl |>
      tidy_combined_autoplot()

    t <- rnbinom(50, 1, .1)
    util_negative_binomial_param_estimate(t, .size = 1)$parameter_tbl
    #> # A tibble: 2 × 9
    #>   dist_type         samp_size   min   max  mean method    size  prob shape_ratio
    #>   <chr>                 <int> <dbl> <dbl> <dbl> <chr>    <dbl> <dbl>       <dbl>
    #> 1 Negative Binomial        50     0    21  7.36 EnvStat…    50 0.120        418
    #> 2 Negative Binomial        50     0    21  7.36 EnvStat…    50 0.118        426.