
Compare Empirical Data to Distributions
Source:R/utils-distribution-comparison.R
tidy_distribution_comparison.Rd
Compare some empirical data set against different distributions to help find the distribution that could be the best fit.
Arguments
- .x
The data set being passed to the function
- .distribution_type
What kind of data is it, can be one of
continuous
ordiscrete
- .round_to_place
How many decimal places should the parameter estimates be rounded off to for distibution construction. The default is 3
Details
The purpose of this function is to take some data set provided and
to try to find a distribution that may fit the best. A parameter of
.distribution_type
must be set to either continuous
or discrete
in order
for this the function to try the appropriate types of distributions.
The following distributions are used:
Continuous:
tidy_beta
tidy_cauchy
tidy_exponential
tidy_gamma
tidy_logistic
tidy_lognormal
tidy_normal
tidy_pareto
tidy_uniform
tidy_weibull
Discrete:
tidy_binomial
tidy_geometric
tidy_hypergeometric
tidy_poisson
The function itself returns a list output of tibbles. Here are the tibbles that are returned:
comparison_tbl
deviance_tbl
total_deviance_tbl
aic_tbl
kolmogorov_smirnov_tbl
multi_metric_tbl
The comparison_tbl
is a long tibble
that lists the values of the density
function against the given data.
The deviance_tbl
and the total_deviance_tbl
just give the simple difference
from the actual density to the estimated density for the given estimated distribution.
The aic_tbl
will provide the AIC
for a lm
model of the estimated density
against the emprical density.
The kolmogorov_smirnov_tbl
for now provides a two.sided
estimate of the
ks.test
of the estimated density against the empirical.
The multi_metric_tbl
will summarise all of these metrics into a single tibble.
Examples
xc <- mtcars$mpg
output_c <- tidy_distribution_comparison(xc, "continuous")
#> For the beta distribution, its mean 'mu' should be 0 < mu < 1. The data will
#> therefore be scaled to enforce this.
xd <- trunc(xc)
output_d <- tidy_distribution_comparison(xd, "discrete")
output_c
#> $comparison_tbl
#> # A tibble: 352 × 8
#> sim_number x y dx dy p q dist_type
#> <fct> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <fct>
#> 1 1 1 21 2.97 0.000114 0.625 10.4 Empirical
#> 2 1 2 21 4.21 0.000455 0.625 10.4 Empirical
#> 3 1 3 22.8 5.44 0.00142 0.781 13.3 Empirical
#> 4 1 4 21.4 6.68 0.00355 0.688 14.3 Empirical
#> 5 1 5 18.7 7.92 0.00721 0.469 14.7 Empirical
#> 6 1 6 18.1 9.16 0.0124 0.438 15 Empirical
#> 7 1 7 14.3 10.4 0.0192 0.125 15.2 Empirical
#> 8 1 8 24.4 11.6 0.0281 0.812 15.2 Empirical
#> 9 1 9 22.8 12.9 0.0395 0.781 15.5 Empirical
#> 10 1 10 19.2 14.1 0.0516 0.531 15.8 Empirical
#> # ℹ 342 more rows
#>
#> $deviance_tbl
#> # A tibble: 352 × 2
#> name value
#> <chr> <dbl>
#> 1 Empirical 0.451
#> 2 Beta c(1.107, 1.577, 0) 0.287
#> 3 Cauchy c(19.2, 7.375) -0.0169
#> 4 Exponential c(0.05) 0.133
#> 5 Gamma c(11.47, 1.752) -0.254
#> 6 Logistic c(20.091, 3.27) -0.0146
#> 7 Lognormal c(2.958, 0.293) 0.315
#> 8 Pareto c(10.4, 1.624) 0.412
#> 9 Uniform c(8.341, 31.841) 0.143
#> 10 Weibull c(3.579, 22.288) -0.201
#> # ℹ 342 more rows
#>
#> $total_deviance_tbl
#> # A tibble: 10 × 2
#> dist_with_params abs_tot_deviance
#> <chr> <dbl>
#> 1 Beta c(1.107, 1.577, 0) 0.640
#> 2 Lognormal c(2.958, 0.293) 0.734
#> 3 Gaussian c(20.091, 5.932) 1.39
#> 4 Cauchy c(19.2, 7.375) 1.56
#> 5 Logistic c(20.091, 3.27) 2.79
#> 6 Uniform c(8.341, 31.841) 2.99
#> 7 Weibull c(3.579, 22.288) 3.34
#> 8 Pareto c(10.4, 1.624) 3.77
#> 9 Gamma c(11.47, 1.752) 4.06
#> 10 Exponential c(0.05) 7.08
#>
#> $aic_tbl
#> # A tibble: 10 × 3
#> dist_type aic_value abs_aic
#> <fct> <dbl> <dbl>
#> 1 Beta c(1.107, 1.577, 0) -22.4 22.4
#> 2 Pareto c(10.4, 1.624) 85.6 85.6
#> 3 Gamma c(11.47, 1.752) -155. 155.
#> 4 Logistic c(20.091, 3.27) -161. 161.
#> 5 Gaussian c(20.091, 5.932) -172. 172.
#> 6 Weibull c(3.579, 22.288) -181. 181.
#> 7 Cauchy c(19.2, 7.375) -189. 189.
#> 8 Exponential c(0.05) -204. 204.
#> 9 Lognormal c(2.958, 0.293) -207. 207.
#> 10 Uniform c(8.341, 31.841) -208. 208.
#>
#> $kolmogorov_smirnov_tbl
#> # A tibble: 10 × 6
#> dist_type ks_statistic ks_pvalue ks_method alternative dist_char
#> <fct> <dbl> <dbl> <chr> <chr> <chr>
#> 1 Beta c(1.107, 1.577, … 0.75 0.000500 Monte-Ca… two-sided Beta c(1…
#> 2 Cauchy c(19.2, 7.375) 0.469 0.00100 Monte-Ca… two-sided Cauchy c…
#> 3 Exponential c(0.05) 0.5 0.00100 Monte-Ca… two-sided Exponent…
#> 4 Gamma c(11.47, 1.752) 0.156 0.839 Monte-Ca… two-sided Gamma c(…
#> 5 Logistic c(20.091, 3.… 0.125 0.970 Monte-Ca… two-sided Logistic…
#> 6 Lognormal c(2.958, 0.… 0.219 0.444 Monte-Ca… two-sided Lognorma…
#> 7 Pareto c(10.4, 1.624) 0.844 0.000500 Monte-Ca… two-sided Pareto c…
#> 8 Uniform c(8.341, 31.8… 0.25 0.269 Monte-Ca… two-sided Uniform …
#> 9 Weibull c(3.579, 22.2… 0.188 0.646 Monte-Ca… two-sided Weibull …
#> 10 Gaussian c(20.091, 5.… 0.188 0.658 Monte-Ca… two-sided Gaussian…
#>
#> $multi_metric_tbl
#> # A tibble: 10 × 8
#> dist_type abs_tot_deviance aic_value abs_aic ks_statistic ks_pvalue ks_method
#> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
#> 1 Beta c(1… 0.640 -22.4 22.4 0.75 0.000500 Monte-Ca…
#> 2 Lognorma… 0.734 -207. 207. 0.219 0.444 Monte-Ca…
#> 3 Gaussian… 1.39 -172. 172. 0.188 0.658 Monte-Ca…
#> 4 Cauchy c… 1.56 -189. 189. 0.469 0.00100 Monte-Ca…
#> 5 Logistic… 2.79 -161. 161. 0.125 0.970 Monte-Ca…
#> 6 Uniform … 2.99 -208. 208. 0.25 0.269 Monte-Ca…
#> 7 Weibull … 3.34 -181. 181. 0.188 0.646 Monte-Ca…
#> 8 Pareto c… 3.77 85.6 85.6 0.844 0.000500 Monte-Ca…
#> 9 Gamma c(… 4.06 -155. 155. 0.156 0.839 Monte-Ca…
#> 10 Exponent… 7.08 -204. 204. 0.5 0.00100 Monte-Ca…
#> # ℹ 1 more variable: alternative <chr>
#>
#> attr(,".x")
#> [1] 21.0 21.0 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 17.8 16.4 17.3 15.2 10.4
#> [16] 10.4 14.7 32.4 30.4 33.9 21.5 15.5 15.2 13.3 19.2 27.3 26.0 30.4 15.8 19.7
#> [31] 15.0 21.4
#> attr(,".n")
#> [1] 32