Warning: package 'tidyverse' was built under R version 4.5.2
Warning: package 'ggplot2' was built under R version 4.5.2
── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr 1.1.4 ✔ readr 2.1.5
✔ forcats 1.0.0 ✔ stringr 1.5.1
✔ ggplot2 4.0.1 ✔ tibble 3.3.0
✔ lubridate 1.9.4 ✔ tidyr 1.3.1
✔ purrr 1.1.0
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
Attaching package: 'purrrfect'
The following objects are masked from 'package:base':
replicate, tabulate
# 3 Pops : UNIF(0,8) ; GAM(alpha = 2, beta = 2) ; POI(4) # Unif Sim head (unif_sim <- parameters (~ n, c (5 , 10 , 20 , 40 , 80 , 160 )) %>% add_trials (10000 ) %>% mutate (y_sample = map (n, ~ runif (.x, 0 , 8 )),y_bar = map_dbl (y_sample, mean)%>% mutate (fU = dnorm (y_bar, mean = 4 , sd = 2.3094 / sqrt (n)),FU = pnorm (y_bar, mean = 4 , sd = 2.3094 / sqrt (n)),Fhat = cume_dist (y_bar),.by = n
# A tibble: 6 × 7
n .trial y_sample y_bar fU FU Fhat
<dbl> <dbl> <list> <dbl> <dbl> <dbl> <dbl>
1 5 1 <dbl [5]> 4.77 0.292 0.773 0.766
2 5 2 <dbl [5]> 6.68 0.0135 0.995 0.998
3 5 3 <dbl [5]> 1.78 0.0385 0.0159 0.0123
4 5 4 <dbl [5]> 4.05 0.386 0.520 0.522
5 5 5 <dbl [5]> 3.74 0.374 0.400 0.403
6 5 6 <dbl [5]> 2.94 0.228 0.152 0.158
# UNIF(0,8) pdf and CDF Overlay #pdf ggplot (unif_sim, aes (x = y_bar)) + geom_histogram (aes (y = after_stat (density)), binwidth = .1 , fill = 'cornflowerblue' ) + geom_line (aes (y = fU), col = 'red' ) + facet_wrap (~ n, scales = 'free_y' ) + labs (title = "Uniform(0,8)" , x = expression (bar (Y))) + theme_classic ()#cdf ggplot (unif_sim, aes (x = y_bar)) + geom_line (aes (y = Fhat), col = 'cornflowerblue' , linewidth = 1 ) + geom_line (aes (y = FU), col = 'red' , linetype = "dashed" ) + facet_wrap (~ n, scales = 'free_x' ) + labs (title = "Uniform(0,8): CDF" , x = 'Ybar' ) + theme_classic ()# GAM Sim head (gam_sim <- parameters (~ n, c (5 , 10 , 20 , 40 , 80 , 160 )) %>% add_trials (10000 ) %>% mutate (y_sample = map (n, ~ rgamma (.x, shape = 2 , rate = 2 )),y_bar = map_dbl (y_sample, mean)%>% mutate (fU = dnorm (y_bar, mean = 1 , sd = 0.7071 / sqrt (n)),FU = pnorm (y_bar, mean = 1 , sd = 0.7071 / sqrt (n)),Fhat = cume_dist (y_bar),.by = n
# A tibble: 6 × 7
n .trial y_sample y_bar fU FU Fhat
<dbl> <dbl> <list> <dbl> <dbl> <dbl> <dbl>
1 5 1 <dbl [5]> 1.54 0.293 0.956 0.944
2 5 2 <dbl [5]> 0.889 1.19 0.363 0.394
3 5 3 <dbl [5]> 0.621 0.615 0.115 0.0921
4 5 4 <dbl [5]> 0.479 0.325 0.0498 0.0232
5 5 5 <dbl [5]> 0.723 0.860 0.191 0.193
6 5 6 <dbl [5]> 0.751 0.925 0.215 0.222
# GAM(shape = 2, rate = 2) pdf and CDF Overlay #pdf ggplot (gam_sim, aes (x = y_bar)) + geom_histogram (aes (y = after_stat (density)), binwidth = .05 , fill = 'cornflowerblue' ) + geom_line (aes (y = fU), col = 'red' ) + facet_wrap (~ n, scales = 'free_y' ) + labs (title = "Gamma(2,2)" , x = 'Ybar' ) + theme_classic ()#cdf ggplot (gam_sim, aes (x = y_bar)) + geom_line (aes (y = Fhat), col = 'cornflowerblue' , linewidth = 1 ) + geom_line (aes (y = FU), col = 'red' , linetype = "dashed" ) + facet_wrap (~ n, scales = 'free_x' ) + labs (title = "GAM(2,2): CDF" , x = 'Ybar' ) + theme_classic ()# POI Sim head (poi_sim <- parameters (~ n, c (5 , 10 , 20 , 40 , 80 , 160 )) %>% add_trials (10000 ) %>% mutate (y_sample = map (n, ~ rpois (.x, lambda = 4 )),y_bar = map_dbl (y_sample, mean)%>% mutate (fU = dnorm (y_bar, mean = 4 , sd = 2 / sqrt (n)),FU = pnorm (y_bar, mean = 4 , sd = 2 / sqrt (n)),Fhat = cume_dist (y_bar),.by = n
# A tibble: 6 × 7
n .trial y_sample y_bar fU FU Fhat
<dbl> <dbl> <list> <dbl> <dbl> <dbl> <dbl>
1 5 1 <int [5]> 3.8 0.435 0.412 0.478
2 5 2 <int [5]> 2.8 0.181 0.0899 0.105
3 5 3 <int [5]> 5.6 0.0901 0.963 0.968
4 5 4 <int [5]> 4.2 0.435 0.588 0.648
5 5 5 <int [5]> 4.6 0.356 0.749 0.79
6 5 6 <int [5]> 2.2 0.0589 0.0221 0.0221
# POI(4) pdf and CDF Overlay #pdf ggplot (poi_sim, aes ( x = y_bar)) + geom_histogram (aes (y = after_stat (density)), binwidth = 0.2 , fill = 'cornflowerblue' ) + geom_line (aes (y= fU), col= 'red' ) + facet_wrap (~ n, scales = 'free_y' ) + labs (title = 'POI(4)' , x = 'Ybar' ) + theme_classic ()#cdf ggplot (poi_sim, aes (x = y_bar)) + geom_line (aes (y = Fhat), col = 'cornflowerblue' , linewidth = 1 ) + geom_line (aes (y = FU), col = 'red' , linetype = "dashed" ) + facet_wrap (~ n, scales = 'free_x' ) + labs (title = "POI(4): CDF" , x = 'Ybar' ) + theme_classic ()
