Test: Normal - PDF

Ivan Jacob Agaloos Pesigan

2020-08-06

Source: vignettes/tests/test_norm_pdf.Rmd 
library(testthat)
library(microbenchmark)
library(jeksterslabRdist)
context("Test Normal - PDF.")

Parameters

n <- 50
mu <- runif(
  n = 1,
  min = 1,
  max = 2
)
sigma <- runif(
  n = 1,
  min = 1,
  max = 2
)
Variable <- c(
  "`n`",
  "`mu`",
  "`sigma`"
)
Description <- c(
  "Sample size ($n$).",
  "Population mean ($\\mu$).",
  "Population standard deviation ($\\sigma$)."
)
Value <- c(
  n,
  mu,
  sigma
)
knitr::kable(
  x = data.frame(
    Variable,
    Description,
    Value
  ),
  row.names = FALSE
)
Variable Description Value
n Sample size (\(n\)). 50.000000
mu Population mean (\(\mu\)). 1.657560
sigma Population standard deviation (\(\sigma\)). 1.726645

Generate Data

x <- rnorm(
  n = n,
  mean = mu,
  sd = sigma
)
x_bar <- mean(x)
s <- sd(x)
Variable <- c(
  "`n`",
  "`x_bar`",
  "`s`"
)
Description <- c(
  "Sample size ($n$).",
  "Samnple mean ($\\bar{x}$).",
  "Sample standard deviation ($s$)."
)
Value <- c(
  n,
  x_bar,
  s
)
knitr::kable(
  x = data.frame(
    Variable,
    Description,
    Value
  ),
  row.names = FALSE
)
Variable Description Value
n Sample size (\(n\)). 50.000000
x_bar Samnple mean (\(\bar{x}\)). 1.358318
s Sample standard deviation (\(s\)). 1.772847

Probability Density Function

results_dnorm <- dnorm(
  x = x,
  mean = mu,
  sd = sigma,
  log = FALSE
)
results_normpdf <- normpdf(
  x = x,
  mu = mu,
  sigma = sigma,
  log = FALSE
)
results_dnorm_log <- dnorm(
  x = x,
  mean = mu,
  sd = sigma,
  log = TRUE
)
results_normpdf_log <- normpdf(
  x = x,
  mu = mu,
  sigma = sigma,
  log = TRUE
)
plot(
  x = x,
  y = results_normpdf
)

plot(
  x = x,
  y = results_dnorm
)

plot(
  x = x,
  y = results_normpdf_log
)

plot(
  x = x,
  y = results_dnorm_log
)

Summarize Results

knitr::kable(
  x = data.frame(
    x = x,
    dnorm = results_dnorm,
    normpdf = results_normpdf,
    dnorm_log = results_dnorm_log,
    normpdf_log = results_normpdf_log
  ),
  row.names = FALSE
)
x dnorm normpdf dnorm_log normpdf_log
-0.9191417 0.0758784 0.0758784 -2.578624 -2.578624
3.7172006 0.1134296 0.1134296 -2.176573 -2.176573
1.7876530 0.2303957 0.2303957 -1.467957 -1.467957
0.4532147 0.1811598 0.1811598 -1.708376 -1.708376
0.1472122 0.1576000 0.1576000 -1.847695 -1.847695
-0.2138225 0.1284189 0.1284189 -2.052458 -2.052458
0.3726174 0.1751655 0.1751655 -1.742024 -1.742024
-0.6986924 0.0910595 0.0910595 -2.396243 -2.396243
1.7642812 0.2306096 0.2306096 -1.467029 -1.467029
-0.5033766 0.1055813 0.1055813 -2.248274 -2.248274
0.0043296 0.1460942 0.1460942 -1.923504 -1.923504
0.7706340 0.2024936 0.2024936 -1.597047 -1.597047
4.1340415 0.0826046 0.0826046 -2.493689 -2.493689
-0.0355401 0.1428615 0.1428615 -1.945880 -1.945880
3.1808372 0.1565667 0.1565667 -1.854273 -1.854273
3.0325584 0.1682678 0.1682678 -1.782198 -1.782198
2.6675715 0.1947175 0.1947175 -1.636206 -1.636206
-1.7476934 0.0330457 0.0330457 -3.409864 -3.409864
-0.2192841 0.1279787 0.1279787 -2.055891 -2.055891
0.1145370 0.1549849 0.1549849 -1.864427 -1.864427
2.7390140 0.1898986 0.1898986 -1.661265 -1.661265
3.0602823 0.1661086 0.1661086 -1.795114 -1.795114
4.1875262 0.0789771 0.0789771 -2.538597 -2.538597
4.4392023 0.0631151 0.0631151 -2.762795 -2.762795
1.8555426 0.2295366 0.2295366 -1.471693 -1.471693
0.5048483 0.1848954 0.1848954 -1.687965 -1.687965
3.0282942 0.1685986 0.1685986 -1.780235 -1.780235
0.6866873 0.1972659 0.1972659 -1.623203 -1.623203
-1.5151201 0.0427114 0.0427114 -3.153290 -3.153290
0.1224199 0.1556169 0.1556169 -1.860358 -1.860358
3.5439051 0.1272136 0.1272136 -2.061888 -2.061888
0.2054902 0.1622300 0.1622300 -1.818740 -1.818740
-0.3520125 0.1173724 0.1173724 -2.142403 -2.142403
2.8109510 0.1848468 0.1848468 -1.688228 -1.688228
2.4922556 0.2055704 0.2055704 -1.581967 -1.581967
0.1177275 0.1552408 0.1552408 -1.862778 -1.862778
-1.9587432 0.0257738 0.0257738 -3.658396 -3.658396
0.6905769 0.1975154 0.1975154 -1.621939 -1.621939
3.8955529 0.0997466 0.0997466 -2.305123 -2.305123
0.3245913 0.1715106 0.1715106 -1.763110 -1.763110
1.2462778 0.2245880 0.2245880 -1.493488 -1.493488
1.7260982 0.2308686 0.2308686 -1.465907 -1.465907
2.3313923 0.2141094 0.2141094 -1.541268 -1.541268
3.0432495 0.1674370 0.1674370 -1.787148 -1.787148
2.2457766 0.2180247 0.2180247 -1.523147 -1.523147
1.4348746 0.2291370 0.2291370 -1.473435 -1.473435
0.3933793 0.1767272 0.1767272 -1.733148 -1.733148
2.1692434 0.2211246 0.2211246 -1.509029 -1.509029
5.3806781 0.0225984 0.0225984 -3.789876 -3.789876
-0.7432199 0.0878814 0.0878814 -2.431767 -2.431767

Benchmarking

microbenchmark(
  dnorm = dnorm(x = x, mean = mu, sd = sigma, log = FALSE),
  normpdf = normpdf(x = x, mu = mu, sigma = sigma, log = FALSE),
  dnorm_log = dnorm(x = x, mean = mu, sd = sigma, log = TRUE),
  normpdf_log = normpdf(x = x, mu = mu, sigma = sigma, log = TRUE)
)
#> Unit: microseconds
#>         expr   min     lq    mean median     uq    max neval
#>        dnorm 1.674 1.9355 2.60573  2.197 3.1140 13.656   100
#>      normpdf 1.461 1.6505 2.40606  1.893 3.0380 13.124   100
#>    dnorm_log 1.338 1.5185 2.07308  1.737 2.7785  3.852   100
#>  normpdf_log 1.849 2.1495 2.96810  2.377 3.8700 14.221   100

testthat

test_that("normpdf return the same values as dnorm", {
  expect_equivalent(
    round(
      x = results_dnorm,
      digits = 2
    ),
    round(
      x = results_normpdf,
      digits = 2
    )
  )
})
test_that("normpdf log = TRUE return the same values as dnorm log = TRUE", {
  expect_equivalent(
    round(
      x = results_dnorm_log,
      digits = 2
    ),
    round(
      x = results_normpdf_log,
      digits = 2
    )
  )
})