Normal density (C backend)

Evaluates the density of the normal distribution with a given mean and standard deviation at each value of x, in compiled code. It is the same kernel that other packages reach through LinkingTo: rmoriebricklayer, and for a positive standard deviation it agrees with dnorm.

Usage

cnormpdf(x, mean = 0, sd = 1)

Arguments

x

Numeric vector of quantiles at which the density is evaluated.

mean

Number, default 0: the mean \(\mu\).

sd

Number, default 1: the standard deviation \(\sigma\); must be positive for a finite result.

Value

A numeric vector the length of x.

Details

$$f(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp\left(-\frac{(x - \mu)^2}{2\sigma^2}\right).$$ The function is vectorised over x only; mean must be a single finite number and sd a single positive number, and anything else is an error (dnorm() recycles them, and gives Inf or NaN for sd = 0 or below). NA in x gives NA; x = Inf gives 0. Character, factor or list input for x is an error.

See also

cstat, dnorm.

Examples

# Standard normal density at a few quantiles.
cnormpdf(c(-1, 0, 1))
#> [1] 0.2419707 0.3989423 0.2419707

# Peak of the standard normal is 1/sqrt(2*pi) at x = 0.
cnormpdf(0)
#> [1] 0.3989423

# Shift and scale via mean and sd.
cnormpdf(c(0, 5, 10), mean = 5, sd = 2)
#> [1] 0.00876415 0.19947114 0.00876415

# Identical to stats::dnorm().
all.equal(cnormpdf(-2:2, 0, 1), stats::dnorm(-2:2, 0, 1))
#> [1] TRUE

# a non-positive sd and text are refused
try(cnormpdf(0, sd = 0))
#> Error : cnormpdf: `sd` must be a single positive number
try(cnormpdf("0"))
#> Error : cnormpdf: `x` must be numeric, got character