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20.4.7  Normal distributions

The probability density function for a normal distribution.

The density function of the normal distribution with mean µ and standard deviation σ at the point x is

normald(µ,σ,x)=
1
 σ
 e(x−µ)2/2.     (4)

The normald (or loi_normal) command finds the value of this density function.

Examples

normald(2,1,3)
     
e
1
2
 
2 π 
          
normald(2)
     
1
2 π 
 e2
          
The cumulative distribution function for normal distribution.

The normal_cdf (or normald_cdf) command computes the cumulative distribution function for the normal distribution.

Examples

normal_cdf(1,2,1.96)
     
0.684386303484           
normal_cdf(1,2.1,1.2)
     
0.537937144066           
normal_cdf(1,2.1,1.2,9)
     
0.461993238584           
The inverse distribution function for normal distribution.

The normal_icdf (or normald_icdf) command computes the inverse distribution for the normal distribution.

Examples

normal_icdf(0.975)
     
1.95996398454           
normal_icdf(1,2,0.495)
     
0.974933060984           
The upper tail cumulative function for normal distributions.

The UTPN (the Upper Tail Probability-Normal distribution) computes Prob(X > x) for a normal distribution.

Examples

UTPN(1.96)
     
0.0249978951482           
UTPN(1,4,1.96)
     
0.315613696516           

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