## 12.9 The `stats` module

The `stats` module contains statistical functions:

**stats.binomialCDF()**

The stats.binomialCDF() function evaluates the probability of getting fewer than or exactly successes out of trials in a binomial distribution with success probability . and must be positive real integers. must be a real number in the range .

**stats.binomialPDF()**

The stats.binomialPDF() function evaluates the probability of getting successes out of trials in a binomial distribution with success probability . and must be positive real integers. must be a real number in the range .

**stats.chisqCDF()**

The stats.chisqCDF() function returns the cumulative probability density at in a -squared distribution with degrees of freedom. must be a positive real dimensionless integer. must be a positive real dimensionless number.

**stats.chisqCDFi()**

The stats.chisqCDFi() function returns the point at which the cumulative probability density in a -squared distribution with degrees of freedom is . must be a positive real dimensionless integer. must be a real number in the range .

**stats.chisqPDF()**

The stats.chisqPDF() function returns the probability density at in a -squared distribution with degrees of freedom. must be a positive real dimensionless integer. must be a positive real dimensionless number.

**stats.gaussianCDF()**

The stats.gaussianCDF() function evaluates the Gaussian cumulative distribution function of standard deviation at . The distribution is centred upon . and must both be real, but may have any physical dimensions so long as they match.

**stats.gaussianCDFi()**

The stats.gaussianCDFi() function evaluates the inverse Gaussian cumulative distribution function of standard deviation at . The distribution is centred upon . and must both be real, but may have any physical dimensions so long as they match.

**stats.gaussianPDF()**

The stats.gaussianPDF() function evaluates the Gaussian probability density function of standard deviation at . The distribution is centred upon . and must both be real, but may have any physical dimensions so long as they match.

**stats.lognormalCDF()**

The stats.lognormalCDF() function evaluates the log normal cumulative distribution function of standard deviation , centred upon , at . must be real, positive and dimensionless. and must both be real, but may have any physical dimensions so long as they match.

**stats.lognormalCDFi()**

The stats.lognormalCDFi() function evaluates the inverse log normal cumulative distribution function of standard deviation , centred upon , at . must be real, positive and dimensionless. and must both be real, but may have any physical dimensions so long as they match.

**stats.lognormalPDF()**

The stats.lognormalPDF() function evaluates the log normal probability density function of standard deviation , centred upon , at . must be real, positive and dimensionless. and must both be real, but may have any physical dimensions so long as they match.

**stats.poissonCDF()**

The stats.poissonCDF() function returns the probability of getting from a Poisson distribution with mean , where must be real, positive and dimensionless and must be real and dimensionless.

**stats.poissonPDF()**

The stats.poissonPDF() function returns the probability of getting from a Poisson distribution with mean , where must be real, positive and dimensionless and must be a real dimensionless integer.

**stats.tdistCDF()**

The stats.tdistCDF() function returns the cumulative probability density at in a -distribution with degrees of freedom. must be a positive real dimensionless integer. must be a positive real dimensionless number.

**stats.tdistCDFi()**

The stats.tdistCDFi() function returns the point at which the cumulative probability density in a -distribution with degrees of freedom is . must be a positive real dimensionless integer. must be a real number in the range .

**stats.tdistPDF()**

The stats.tdistPDF() function returns the probability density at in a -distribution with degrees of freedom. must be a positive real dimensionless integer. must be a positive real dimensionless number.