| 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)2 | invttail(df,p)3 | ||
| F | F(df1,df2,F) | invF(df1,df2,p) | ||
| Chi-square | chi2(df,x) | invchi2(df,p) | ||
| Chi-square (non-central)1 | nchi2(df,l,x) | invnchi2(df,l,p) | ||
| Gamma | gammap(a,x) | invgamma(a,p) | ||
| Beta | ||||
| 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 are non-standard)
1. Not available in SYSTAT.
2. ttail(df,t) is the reverse cumulative t distribution P(T>t)
3. invttail is "inverse cumulative" (?)
4. 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"
5. invbinomial(n,k,p) (?)