The normald (or loi_normal) command returns the value of the normal probability density function. You can give it arguments of the mean µ, standard deviation σ and a value x then
normald(µ,σ,x) = |
| e(x−µ)2/2 |
If you enter
you will get
If you don’t give the command values for µ and σ, then normald will use the values µ=0 and σ = 1, and so compute the standard normal density function. If you enter
you will get
The command normal_cdf (or normald_cdf) computes the cumulative distribution function for the normal distribution. Like normald, you can give it the mean and standard deviation of the distribution; if you enter
you will get
You can also leave off the mean and standard deviation, in which case normal_cdf will compute the cumulative distribution function for the standard normal distribution;
you will get
If you give normal_cdf an extra argument (with or without the mean and standard deviation), you will get the probability that the random variable lies between two values; normal_cdf(x,y) = Prob(x ≤ X ≤ y). If you enter
you will get
Given a value h, the inverse distribution function gives the value of x with Prob(X ≤ x) ≤ h. The normal_icdf (or normald_icdf) will compute the inverse distribution for the normal distribution. If no mean or standard deviation are given, the standard normal distribution will be used. If you enter
you will get
You can, of course, also give the mean and standard deviation. If you enter
you will get
The UTPN (the Upper Tail Probability - Normal distribution) will compute Prob(X > x). If you don’t give it a mean and variance, then it will compute the probability for the standard normal distribution. If you enter
you will get
You can also specify a mean and a variance, but note that unlike normald and normal_cdf, the UTPN requires the variance and not the standard deviation. If you enter
you will get