normpdf: Normal Distribution - Probablity Density Function

In jeksterslabds/jeksterslabRdist: Jekster's Lab Distribution Utilities

Description

Calculates probablities from the probability density function of the normal distribution X \sim \mathcal{N} ≤ft( μ, σ^2 \right) %(\#eq:dist-X-norm) . This function is identical to dnorm().

Usage

normpdf(x, mu = 0, sigma = 1, log = FALSE)

Arguments

x	Numeric vector. Values of the random variable X.
mu	Numeric. Location parameter mean μ.
sigma	Numeric. Positive number. Scale parameter standard deviation σ = √{σ^2}.
log	Logical. If TRUE, returns \log ≤ft( f ≤ft( x \right) \right).

Details

The normal (or Gaussian or Gauss or Laplace–Gauss) distribution is given by

X \sim \mathcal{N} ≤ft( μ, σ^2 \right) %(\#eq:dist-X-norm)

and has the probability density function (PDF)

f ≤ft( x \right) = \frac{1}{σ √{2 π}} \exp ≤ft[ - \frac{1}{2} ≤ft( \frac{x - μ}{σ} \right)^2 \right] %(\#eq:dist-normpdf-1)

or

f ≤ft( x \right) = \frac{1}{√{2 π σ^2}} \exp ≤ft[ - \frac{ ≤ft( x - μ \right)^2} {2 σ^2} \right] %(\#eq:dist-normpdf-2)

with

• x \in \mathbf{R},

• μ is the location parameter mean ≤ft( μ \in \mathbf{R} \right), and

• σ^2 is the scale parameter variance ≤ft( σ^2 > 0 \right).

Value

Returns f ≤ft( x \right) using the probablity density function with the supplied parameter/s. If log = TRUE, returns \log ≤ft( f ≤ft( x \right) \right).

Author(s)

Ivan Jacob Agaloos Pesigan

References

Wikipedia: Normal Distribution

See Also

Other normal likelihood functions: norm2ll(), normL(), normll(), normobj()

jeksterslabds/jeksterslabRdist documentation built on Aug. 9, 2020, 7:33 a.m.