@spec cdf() :: (... -> any())

The cumulative density function

The probability that a value lies below x

Cumulative gives a probability that a statistic is less than Z. This equates to the area of the distribution below Z. e.g: Pr(Z = 0.69) = 0.7549. This value is usually given in Z tables.

Examples

iex> Statistics.Distributions.Normal.cdf().(2) 0.9772499371127437 iex> Statistics.Distributions.Normal.cdf(0,1).(0) 0.5000000005

@spec pdf() :: (... -> any())

Probability density function

Roughly the expectation of a given value in the distribution

Examples

iex> Statistics.Distributions.Normal.pdf().(0)
0.3989422804014327
iex> Statistics.Distributions.Normal.pdf(0.2, 1).(1.3)
0.21785217703255055copy

@spec ppf() :: (... -> any())

The percentile-point function

Get the maximum point which lies below the given probability. This is the inverse of the cdf

Examples

iex> Statistics.Distributions.Normal.ppf().(0.025)
-1.96039491692534
iex> Statistics.Distributions.Normal.ppf(7, 2.1).(0.25)
5.584202805909036copy

@spec rand() :: number()

Draw a random number from a normal distribution

rnd/0 will return a random number from a normal distribution with a mean of 0 and a standard deviation of 1

rnd/2 allows you to provide the mean and standard deviation parameters of the distribution from which the random number is drawn

Uses the rejection sampling method

Examples

iex> Statistics.Distributions.Normal.rand()
1.5990817245679434
iex> Statistics.Distributions.Normal.rand(22, 2.3)
23.900248900049736copy