# cdf¶

Usage 1: cdf [-v] -t2p statname t params
Usage 2: cdf [-v] -p2t statname p params
Usage 3: cdf [-v] -t2z statname t params

This program does various conversions using the cumulative distribution
function (cdf) of certain canonical probability functions.  The optional
'-v' indicates to be verbose -- this is for debugging purposes, mostly.
Use this option if you get results you don't understand!

Usage 1: Converts a statistic 't' to a tail probability.
Usage 2: Converts a tail probability 'p' to a statistic.
Usage 3: Converts a statistic 't' to a N(0,1) value (or z-score)
that has the same tail probability.

The parameter 'statname' refers to the type of distribution to be used.
The numbers in the params list are the auxiliary parameters for the
particular distribution.  The following table shows the available
distribution functions and their parameters:

statname  Description  PARAMETERS
--------  -----------  ----------------------------------------
fico  Cor          SAMPLES  FIT-PARAMETERS  ORT-PARAMETERS
fitt  Ttest        DEGREES-of-FREEDOM
fift  Ftest        NUMERATOR and DENOMINATOR DEGREES-of-FREEDOM
fizt  Ztest        N/A
fict  ChiSq        DEGREES-of-FREEDOM
fibt  Beta         A (numerator) and B (denominator)
fibn  Binom        NUMBER-of-TRIALS and PROBABILITY-per-TRIAL
figt  Gamma        SHAPE and SCALE
fipt  Poisson      MEAN

EXAMPLES:
Goal:    find p-value for t-statistic of 5.5 with 30 degrees of freedom
COMMAND: cdf -t2p fitt 5.5 30
OUTPUT:  p = 5.67857e-06

Goal:    find F(8,200) threshold that gives a p-value of 0.001
COMMAND: cdf -p2t fift 0.001 8 200
OUTPUT:  t = 3.4343

The same functionality is also available in 3dcalc, 1deval, and
ccalc, using functions such as 'fift_t2p(t,a,b)'.  In particular,
if you are scripting, ccalc is probably better to use than cdf,
since the output of
ccalc -expr 'fitt_t2p(3,20)'
is the string '0.007076', while the output of
cdf -t2p fitt 3 20
is the string 'p = 0.0070759'.