Cumulative Distribution Functions

A Cumulative Distribution Function (CDF) is the integral of its respective probability distribution function (PDF). CDFs are usually well behaved functions with values in the range [0,1]. CDFs are important in computing critical values, P-values and power of statistical tests.

Many CDFs are computed directly from closed form expressions. Others can be difficult to compute because they involve evaluating a very large number states, e.g., the CDFs of the Friedman or USquared distributions. In these cases you have the following options:

Built-in tables are ideal if they cover the range of the parameters that you need. Monte-Carlo methods can be tricky in the sense that repeated application may return small variations in values. Computing the exact CDF may be nice but could sometimes be impractical. In most situations the range of parameters that is practical to compute on a desktop machine is already covered in the built-in tables. Larger parameters have not been considered because they may take a long time to compute or because they may require 64 bit processors. In addition, most approximations tend to improve with increasing size of the parameters.

Igor Function Cumulative Distribution Function
StatsBetaCDF Beta
StatsBinomialCDF Binomial
StatsCauchyCDF Cauchy
StatsChiCDF Chi-squared
StatsCMSSDCDF C (mean square successive difference)
StatsDExpCDF Double-exponential
StatsErlangCDF Erlang
StatsEValueCDF Extreme-value (type I Gumble)
StatsExpCDF Exponential
StatsFCDF F
StatsFriedmanCDF Friedman
StatsGammaCDF Gamma
StatsGeometricCDF Geometric
StatsHyperGCDF Hypergeometric
StatsKuiperCDF Kuiper
StatsLogisticCDF Logistic
StatsLogNormalCDF Lognormal
StatsMaxwellCDF Maxwell
StatsMooreCDF Moore
StatsNBinomialCDF Negative Binomial
StatsNCFCDF Non-central F
StatsNCTCDF Non-central Student T
StatsNormalCDF Normal (Gaussian)
StatsParetoCDF Pareto
StatsPoissonCDF Poisson
StatsPowerCDF Power
StatsQCDF Q
StatsRayleighCDF Rayleigh
StatsRectangularCDF Rectangular
StatsRunsCDF Up and Down Runs
StatsSpearmanRhoCDF Spearman's rho
StatsStudentCDF Student-T
StatsTopDownCDF Top-down
StatsTriangularCDF Triangular
StatsUSquaredCDF Watson's U-squared
StatsVonMisesCDF von Mises
StatsWaldCDF Wald
StatsWeibullCDF Weibull