pdf.Normal {distributions3} | R Documentation |

Please see the documentation of `Normal()`

for some properties
of the Normal distribution, as well as extensive examples
showing to how calculate p-values and confidence intervals.

```
## S3 method for class 'Normal'
pdf(d, x, drop = TRUE, elementwise = NULL, ...)
## S3 method for class 'Normal'
log_pdf(d, x, drop = TRUE, elementwise = NULL, ...)
```

`d` |
A |

`x` |
A vector of elements whose probabilities you would like to
determine given the distribution |

`drop` |
logical. Should the result be simplified to a vector if possible? |

`elementwise` |
logical. Should each distribution in |

`...` |
Arguments to be passed to |

In case of a single distribution object, either a numeric
vector of length `probs`

(if `drop = TRUE`

, default) or a `matrix`

with
`length(x)`

columns (if `drop = FALSE`

). In case of a vectorized distribution
object, a matrix with `length(x)`

columns containing all possible combinations.

Other Normal distribution:
`cdf.Normal()`

,
`fit_mle.Normal()`

,
`quantile.Normal()`

```
set.seed(27)
X <- Normal(5, 2)
X
mean(X)
variance(X)
skewness(X)
kurtosis(X)
random(X, 10)
pdf(X, 2)
log_pdf(X, 2)
cdf(X, 4)
quantile(X, 0.7)
### example: calculating p-values for two-sided Z-test
# here the null hypothesis is H_0: mu = 3
# and we assume sigma = 2
# exactly the same as: Z <- Normal(0, 1)
Z <- Normal()
# data to test
x <- c(3, 7, 11, 0, 7, 0, 4, 5, 6, 2)
nx <- length(x)
# calculate the z-statistic
z_stat <- (mean(x) - 3) / (2 / sqrt(nx))
z_stat
# calculate the two-sided p-value
1 - cdf(Z, abs(z_stat)) + cdf(Z, -abs(z_stat))
# exactly equivalent to the above
2 * cdf(Z, -abs(z_stat))
# p-value for one-sided test
# H_0: mu <= 3 vs H_A: mu > 3
1 - cdf(Z, z_stat)
# p-value for one-sided test
# H_0: mu >= 3 vs H_A: mu < 3
cdf(Z, z_stat)
### example: calculating a 88 percent Z CI for a mean
# same `x` as before, still assume `sigma = 2`
# lower-bound
mean(x) - quantile(Z, 1 - 0.12 / 2) * 2 / sqrt(nx)
# upper-bound
mean(x) + quantile(Z, 1 - 0.12 / 2) * 2 / sqrt(nx)
# equivalent to
mean(x) + c(-1, 1) * quantile(Z, 1 - 0.12 / 2) * 2 / sqrt(nx)
# also equivalent to
mean(x) + quantile(Z, 0.12 / 2) * 2 / sqrt(nx)
mean(x) + quantile(Z, 1 - 0.12 / 2) * 2 / sqrt(nx)
### generating random samples and plugging in ks.test()
set.seed(27)
# generate a random sample
ns <- random(Normal(3, 7), 26)
# test if sample is Normal(3, 7)
ks.test(ns, pnorm, mean = 3, sd = 7)
# test if sample is gamma(8, 3) using base R pgamma()
ks.test(ns, pgamma, shape = 8, rate = 3)
### MISC
# note that the cdf() and quantile() functions are inverses
cdf(X, quantile(X, 0.7))
quantile(X, cdf(X, 7))
```

[Package *distributions3* version 0.2.1 Index]