Statistics.Distributions.Normal
The normal, or gaussian, distribution
Summary↑
cdf(x) | Get the probability that a value lies below |
cdf(x, mu, sigma) | |
pdf(x) | Probability density function |
pdf(x, mu, sigma) | |
ppf(x) | The percentile-point function |
ppf(x, mu, sigma) | |
rand() | Draw a random number from a normal distribution |
rand(mu, sigma) |
Functions
Get 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) 0.5000000005
Probability density function
get result of probability density function
Examples
iex> Statistics.Distributions.Normal.pdf(0)
0.3989422804014327
iex> Statistics.Distributions.Normal.pdf(1.3, 0.2, 1)
0.21785217703255055
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(0.25, 7, 2.1)
5.584202805909036
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/3
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)
23.900248900049736