# Estimate Pareto Parameters

Source: `R/est-param-pareto.R`
`util_pareto_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 pareto data.

Two different methods of shape parameters are supplied:

- LSE

- MLE

    util_pareto_estimate(.x, .auto_gen_empirical = TRUE)

## Arguments

.x

  The vector of data to be passed to the function.

.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 pareto shape and scale parameters given some vector of values.

## See also

Other Parameter Estimation: `util_beta_param_estimate()`, `util_binomial_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_negative_binomial_param_estimate()`, `util_normal_param_estimate()`

Other Pareto: `tidy_generalized_pareto()`, `tidy_inverse_pareto()`, `tidy_pareto1()`, `tidy_pareto()`

## Author

Steven P. Sanderson II, MPH

## Examples

    library(dplyr)
    library(ggplot2)

    x <- mtcars$mpg
    output <- util_pareto_estimate(x)

    output$parameter_tbl
    #> # A tibble: 2 x 8
    #>   dist_type samp_size   min   max method shape scale shape_ratio
    #>   <chr>         <int> <dbl> <dbl> <chr>  <dbl> <dbl>       <dbl>
    #> 1 Pareto           32  10.4  33.9 LSE     13.7  2.86        4.79
    #> 2 Pareto           32  10.4  33.9 MLE     10.4  1.62        6.40

    output$combined_data_tbl %>%
      ggplot(aes(x = dx, y = dy, group = dist_type, color = dist_type)) +
      geom_line() +
      theme_minimal() +
      theme(legend.position = "bottom")

    t <- tidy_pareto(50, 1, 1) %>% pull(y)
    util_pareto_estimate(t)$parameter_tbl
    #> # A tibble: 2 x 8
    #>   dist_type samp_size    min   max method  shape scale shape_ratio
    #>   <chr>         <int>  <dbl> <dbl> <chr>   <dbl> <dbl>       <dbl>
    #> 1 Pareto           50 0.0105  184. LSE    0.110  0.467      0.236
    #> 2 Pareto           50 0.0105  184. MLE    0.0105 0.224      0.0468