Estimate Chisquare Parameters

This function will attempt to estimate the Chisquare prob parameter given some vector of values .x. 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 Chisquare data.

Usage

util_chisquare_param_estimate(.x, .auto_gen_empirical = TRUE)

Arguments

.x

The vector of data to be passed to the function. Must be non-negative integers.

.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 see if the given vector .x is a numeric vector. It will attempt to estimate the prob parameter of a Chisquare distribution. The function first performs tidyeval on the input data to ensure it's a numeric vector. It then checks if there are at least two data points, as this is a requirement for parameter estimation.

The estimation of the chi-square distribution parameters is performed using maximum likelihood estimation (MLE) implemented with the bbmle package. The negative log-likelihood function is minimized to obtain the estimates for the degrees of freedom (doff) and the non-centrality parameter (ncp). Initial values for the optimization are set based on the sample variance and mean, but these can be adjusted if necessary.

If the estimation fails or encounters an error, the function returns NA for both doff and ncp.

Finally, the function returns a tibble containing the following information:

dist_type

The type of distribution, which is "Chisquare" in this case.

samp_size

The sample size, i.e., the number of data points in the input vector.

min

The minimum value of the data points.

max

The maximum value of the data points.

mean

The mean of the data points.

degrees_of_freedom

The estimated degrees of freedom (doff) for the chi-square distribution.

ncp

The estimated non-centrality parameter (ncp) for the chi-square distribution.

Additionally, if the argument .auto_gen_empirical is set to TRUE (which is the default behavior), the function also returns a combined tibble containing both empirical and chi-square distribution data, obtained by calling tidy_empirical and tidy_chisquare, respectively.

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_f_param_estimate(), util_gamma_param_estimate(), util_generalized_beta_param_estimate(), util_generalized_pareto_param_estimate(), util_geometric_param_estimate(), util_hypergeometric_param_estimate(), util_inverse_burr_param_estimate(), util_inverse_pareto_param_estimate(), util_inverse_weibull_param_estimate(), util_logistic_param_estimate(), util_lognormal_param_estimate(), util_negative_binomial_param_estimate(), util_normal_param_estimate(), util_paralogistic_param_estimate(), util_pareto1_param_estimate(), util_pareto_param_estimate(), util_poisson_param_estimate(), util_t_param_estimate(), util_triangular_param_estimate(), util_uniform_param_estimate(), util_weibull_param_estimate(), util_zero_truncated_binomial_param_estimate(), util_zero_truncated_geometric_param_estimate(), util_zero_truncated_negative_binomial_param_estimate(), util_zero_truncated_poisson_param_estimate()

Other Chisquare: tidy_chisquare(), util_chisquare_stats_tbl()

Author

Steven P. Sanderson II, MPH

Examples

library(dplyr)
library(ggplot2)

tc <- tidy_chisquare(.n = 500, .df = 6, .ncp = 1) |> pull(y)
output <- util_chisquare_param_estimate(tc)
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced
#> Warning: NaNs produced

output$parameter_tbl
#> # A tibble: 1 × 7
#>   dist_type samp_size   min   max  mean   dof   ncp
#>   <chr>         <int> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Chisquare       500 0.242  23.1  6.92  6.08 0.844

output$combined_data_tbl |>
  tidy_combined_autoplot()