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cli::cat_line(res@value)
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## `help(package = "stats", "rnorm")`
### The Normal Distribution
#### Description
Density, distribution function, quantile function and random generation
for the normal distribution with mean equal to `mean` and standard
deviation equal to `sd`.
#### Usage
``` R
dnorm(x, mean = 0, sd = 1, log = FALSE)
pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)
qnorm(p, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)
rnorm(n, mean = 0, sd = 1)
```
#### Arguments
| | |
|----|----|
| `x`, `q` | vector of quantiles. |
| `p` | vector of probabilities. |
| `n` | number of observations. If `length(n) > 1`, the length is taken to be the number required. |
| `mean` | vector of means. |
| `sd` | vector of standard deviations. |
| `log`, `log.p` | logical; if TRUE, probabilities p are given as log(p). |
| `lower.tail` | logical; if TRUE (default), probabilities are `P[X \le x]` otherwise, `P[X > x]`. |
#### Details
If `mean` or `sd` are not specified they assume the default values of
`0` and `1`, respectively.
The normal distribution has density
` f(x) = \frac{1}{\sqrt{2\pi}\sigma} e^{-(x-\mu)^2/2\sigma^2}`
where `\mu` is the mean of the distribution and `\sigma` the standard
deviation.
#### Value
`dnorm` gives the density, `pnorm` gives the distribution function,
`qnorm` gives the quantile function, and `rnorm` generates random
deviates.
The length of the result is determined by `n` for `rnorm`, and is the
maximum of the lengths of the numerical arguments for the other
functions.
The numerical arguments other than `n` are recycled to the length of the
result. Only the first elements of the logical arguments are used.
For `sd = 0` this gives the limit as `sd` decreases to 0, a point mass
at `mu`. `sd < 0` is an error and returns `NaN`.
#### Source
For `pnorm`, based on
Cody, W. D. (1993) Algorithm 715: SPECFUN – A portable FORTRAN package
of special function routines and test drivers. *ACM Transactions on
Mathematical Software* **19**, 22–32.
For `qnorm`, the code is based on a C translation of
Wichura, M. J. (1988) Algorithm AS 241: The percentage points of the
normal distribution. *Applied Statistics*, **37**, 477–484;
[doi:10.2307/2347330](https://doi.org/10.2307/2347330).
which provides precise results up to about 16 digits for `log.p=FALSE`.
For log scale probabilities in the extreme tails, since
<span class="rlang">**R**</span> version 4.1.0, extensively since 4.3.0,
asymptotic expansions are used which have been derived and explored in
Maechler, M. (2022) Asymptotic tail formulas for gaussian quantiles;
[<span class="pkg">DPQ</span>](https://CRAN.R-project.org/package=DPQ)
vignette
<https://CRAN.R-project.org/package=DPQ/vignettes/qnorm-asymp.pdf>.
For `rnorm`, see RNG for how to select the algorithm and for references
to the supplied methods.
#### References
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) *The New S
Language*. Wadsworth & Brooks/Cole.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) *Continuous
Univariate Distributions*, volume 1, chapter 13. Wiley, New York.
#### See Also
Distributions for other standard distributions, including `dlnorm` for
the *Log*normal distribution.
#### Examples
``` R
require(graphics)
dnorm(0) == 1/sqrt(2*pi)
dnorm(1) == exp(-1/2)/sqrt(2*pi)
dnorm(1) == 1/sqrt(2*pi*exp(1))
## Using "log = TRUE" for an extended range :
par(mfrow = c(2,1))
plot(function(x) dnorm(x, log = TRUE), -60, 50,
main = "log { Normal density }")
curve(log(dnorm(x)), add = TRUE, col = "red", lwd = 2)
mtext("dnorm(x, log=TRUE)", adj = 0)
mtext("log(dnorm(x))", col = "red", adj = 1)
plot(function(x) pnorm(x, log.p = TRUE), -50, 10,
main = "log { Normal Cumulative }")
curve(log(pnorm(x)), add = TRUE, col = "red", lwd = 2)
mtext("pnorm(x, log=TRUE)", adj = 0)
mtext("log(pnorm(x))", col = "red", adj = 1)
## if you want the so-called 'error function'
erf <- function(x) 2 * pnorm(x * sqrt(2)) - 1
## (see Abramowitz and Stegun 29.2.29)
## and the so-called 'complementary error function'
erfc <- function(x) 2 * pnorm(x * sqrt(2), lower = FALSE)
## and the inverses
erfinv <- function (x) qnorm((1 + x)/2)/sqrt(2)
erfcinv <- function (x) qnorm(x/2, lower = FALSE)/sqrt(2)
```
Code
btw_tool_docs_help_page("unknown-topic", "dplyr")
Condition
Error in `btw_tool_docs_help_page()`:
! No help page found for topic "unknown-topic" in package dplyr.
i To search in all packages, call `btw_tool_docs_help_page()` with an empty string for `package_name`.
Code
btw_tool_docs_help_page("unknown-topic")
Condition
Error in `btw_tool_docs_help_page()`:
! No help page found for topic "unknown-topic" in all installed packages.
Code
btw_tool_docs_help_page("filter")
Condition
Error in `btw_tool_docs_help_page()`:
! Topic "filter" matched 2 different topics.
i Choose one or submit individual tool calls for each topic.
* {"topic":"filter", "package_name":"dplyr"}
* {"topic":"filter", "package_name":"stats"}
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