| Distribution | Cumulative
F(x) = P(X<=x) |
Density f(x) | Inverse cumulative
F-1(p)={x|P(X<=x)=p} |
Random generator |
| Uniform | uniform() | |||
| Normal (0, 1] | norm(z) |
normden(z) |
invnorm(p) | |
| t | ttail(df,t) | tden(df,t) | invttail(df,p) | |
| F | F(df1,df2,F) | fden(df1,df2,f) | invF(df1,df2,p) | |
| Chi-square | chi2(df,x) chi2tail(df,x) |
invchi2(df,p) invchi2tail(df,p) |
||
| Chi-square (non-central)1 | nchi2(df,l,x) | invnchi2(df,l,p) | ||
| Gamma | gammap(a,x) | gammaden(a,b,g,x) | invgamma(a,p) | |
| Beta | betaden(a,b,x) | |||
| Exponential (0,1) | ||||
| Logistic (0,1) | ||||
| Studentized | ||||
| Weibull | ||||
| Binomial | binomial(n,k,p)4 | invbinomial(n,k,p)5 | ||
| Poisson | 1-gamma(k+1,x) |
NOTES: Functions in red with 'tail' suffix are are
reversed cumulative functions so that ftail(x)=1-F(x)
1. Not available in SYSTAT.
2. binomial(n,k,p) is the probability of "k or more successes in n trials when
the probability of success on a single trial is p"