2.9 The stats module

The stats module contains statistical functions:

stats.binomialCDF($$k,p,n$)$
The stats.binomialCDF($$k,p,n$) function evaluates the probability of getting fewer than or exactly $k$ successes out of $n$ trials in a binomial distribution with success probability $p$. $k$ and $n$ must be positive real integers. $p$ must be a real number in the range $0≤p ≤1$. $

stats.binomialPDF($$k,p,n$)$
The stats.binomialPDF($$k,p,n$) function evaluates the probability of getting $k$ successes out of $n$ trials in a binomial distribution with success probability $p$. $k$ and $n$ must be positive real integers. $p$ must be a real number in the range $0≤p ≤1$. $

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

stats.chisqCDFi($$P,ν$)$
The stats.chisqCDFi($$P,ν$) function returns the point $x$ at which the cumulative probability density in a $χ$-squared distribution with $ν$ degrees of freedom is $P$. $ν$ must be a positive real dimensionless integer. $P$ must be a real number in the range $0≤p ≤1$. $

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

stats.gaussianCDF($$x,σ$)$
The stats.gaussianCDF($$x,σ$) function evaluates the Gaussian cumulative distribution function of standard deviation $σ$ at $x$. The distribution is centred upon $x=0$. $x$ and $σ$ must both be real, but may have any physical dimensions so long as they match. $

stats.gaussianCDFi($$x,σ$)$
The stats.gaussianCDFi($$x,σ$) function evaluates the inverse Gaussian cumulative distribution function of standard deviation $σ$ at $x$. The distribution is centred upon $x=0$. $x$ and $σ$ must both be real, but may have any physical dimensions so long as they match. $

stats.gaussianPDF($$x,σ$)$
The stats.gaussianPDF($$x,σ$) function evaluates the Gaussian probability density function of standard deviation $σ$ at $x$. The distribution is centred upon $x=0$. $x$ and $σ$ must both be real, but may have any physical dimensions so long as they match. $

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

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

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

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

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

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

stats.tdistCDFi($$P,ν$)$
The stats.tdistCDFi($$P,ν$) function returns the point $x$ at which the cumulative probability density in a $t$-distribution with $ν$ degrees of freedom is $P$. $ν$ must be a positive real dimensionless integer. $P$ must be a real number in the range $0≤p ≤1$. $

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