normal

Density
Mean
Variance
Mode

The Normal distribution is an unbounded continuous distribution. It is sometimes called a Gaussian distribution or the bell curve. Because of its property of representing an increasing sum of small, independent errors, the Normal distribution finds many, many uses in statistics. It is wrongly used in many situations. Possibly, the most important test in the fitting of analytical distributions is the elimination of the Normal distribution as a possible candidate.

The Normal distribution is used as an approximation for the Binomial distribution when the values of n, p are in the appropriate range. The Normal distribution is frequently used to represent symmetrical data, but suffers from being unbounded in both directions. If the data is known to have a lower bound, it may be better represented by suitable parameterization of the Lognormal, Weibull or Gamma distributions. If the data is known to have both upper and lower bounds, the Beta distribution can be used, although much work has been done on truncated Normal distributions.

Sample 

sigma =1; mean = 0

normal(double sigma, double mean)

Description

Generates a sample of the Normal distribution.

Parameters

Name Type Description
sigma double the shape parameter = standard deviation
mean double the shift parameter = mean value

Result

Type Description
double the generated sample

normal(double sigma)

Description

Generates a sample of the Normal distribution with mean set to 0. Is equivalent to normal(sigma, 0).

Parameters

Name Type Description
sigma double the shape parameter = standard deviation

Result

Type Description
double the generated sample


normal()

Description

Generates a sample of the Normal distribution with mean set to 0 and sigma set to 1. Is equivalent to normal(1, 0).

Result

Type Description
double the generated sample

normal(double sigma, mean,java.util.Random r)

Description

Generates a sample of the Normal distribution using the specified random number generator.

Parameters

Name Type Description
sigma double the shape parameter = standard deviation
mean double the shift parameter = mean value
r java.util.Random the random number generator

Result

Type Description
double the generated sample