cumF(x,df1,df2 [,lam] [,upper:T or lower:F]), x, df1, df2 and lam REAL, elements of df1 and df2 >i 0 and lam >= 0 |

cumF(Val,df1,df2) computes the probabilities that an F random variable with df1 and df2 degrees of freedom would be less than the elements of the vector, matrix, or array Val. cumF(Val,df1,df2,upper:T) and cumF(Val,df1,df2,lower:F) compute upper tail probabilities. For large Val, the result may preserve significant digits that are lost when computing the upper tail probability by 1 - cumF(Val,df1,df2). cumF(Val,df1,df2,lam [,upper:T or lower:F]) computes similar probabilities for non-central F with noncentrality parameter lam. Any of Val, df1, df2, or lam that are not scalars (single numbers) must be vectors, matrices, or arrays with the same size and shape which will also be the size and shape of the result. The degrees of freedom must be positive REAL numbers (not necessarily integers). Upper tail areas of F can be computed as 1 - cumF(). Examples: Compute P-value for F-statistic following anova(): Cmd> cumF((SS[2]/DF[2])/(SS[5]/DF[5]), DF[2], DF[5], upper:T) Compute 2-tail P-value for test of sigma_1 = sigma_2 based on sample standard deviations s1 and s2 from independent normal samples. Cmd> 2*min(cumF(s1^2/s2^2, n1-1, n2-1), \ cumF(s1^2/s2^2, n1-1, n2-1, upper:T)) # two tail P-value See also invF(), cumbeta(), invbeta().

Gary Oehlert 2003-01-15