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Statistics[Distributions]

  

Normal

  

normal (Gaussian) distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Normal(mu, sigma)

NormalDistribution(mu, sigma)

Parameters

mu

-

distribution mean

sigma

-

scale parameter

Description

• 

The normal distribution is a continuous probability distribution with probability density function given by:

ft=2ⅇtμ22σ22πσ

  

subject to the following conditions:

μ::real,0<σ

• 

The normal variate Normal(mu,sigma) is related to the standardized variate Normal(0,1) by Normal(0,1) ~ (Normal(mu,sigma)-mu)/sigma.

• 

Note that the Normal command is inert and should be used in combination with the RandomVariable command.

Examples

withStatistics&colon;

XRandomVariableNormal&mu;&comma;&sigma;&colon;

PDFX&comma;u

122&ExponentialE;12u&mu;2&sigma;2&pi;&sigma;

(1)

PDFX&comma;0.5

0.3989422802&ExponentialE;0.50000000000.51.&mu;2&sigma;2&sigma;

(2)

MeanX

&mu;

(3)

VarianceX

&sigma;2

(4)

References

  

Evans, Merran; Hastings, Nicholas; and Peacock, Brian.  Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.

  

Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.

  

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.

See Also

Statistics

Statistics[Distributions]

Statistics[RandomVariable]

 


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