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### The Nematrian Function Library Probability Distribution Functions

The Nematrian function library includes a range of tools that are useful for manipulating, analysing and fitting probability distributions, including calculating their moments and other characteristics and creating random variates drawn from them.

See here for a general introduction to the websiteâ€™s current probability distribution coverage. For details of the specific DistributionName input expected by these web functions (including those that involve shift and scale adjustments to the textbook formulation of a given probability distribution then please refer either to those pages or to MnRecognisedProbDists and MnProbDistParamNames.

The web functions available include ones set out in the table below. To see a complete list of functions currently available in the Nematrian online toolkit please go to list of types of available functions or complete list of individual functions.

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Web functionShort description of function
MnBeta4DistCdfReturns the cumulative distribution function of the beta distribution
MnBeta4DistPdfReturns the probability density function of the beta distribution
MnBeta4InvReturns the inverse cdf, i.e. quantile, of the beta distribution
MnBetaDistCdfReturns the cumulative distribution function of the (standard) beta distribution
MnBetaDistPdfReturns the probability density function of the (standard) beta distribution
MnBetaInvReturns the inverse cdf, i.e. quantile, of the (standard) beta distribution
MnJohnsonSUMOMEstimatesReturns the method of moments estimation vector for parameters of a Johnson SU probability distribution for a given dataset
MnProbDistCdfEvaluates the cumulative distribution function for a given probability distribution
MnProbDistCtsBoundedLowerIndicates if a (continuous) probability distribution has a lower bound other than minus infinity
MnProbDistCtsBoundedUpperIndicates if a (continuous) probability distribution has an upper bound other than plus infinity
MnProbDistCtsLowerBoundReturns lower bound of (continuous) probability distribution (if it is bounded below)
MnProbDistCtsUpperBoundReturns upper bound of (continuous) probability distribution (if it is bounded above)
MnProbDistHazardFunctionReturns the hazard function for a given probability distribution
MnProbDistIsCtsReturns true if probability distribution is continuous, false if it is discrete
MnProbDistKurtReturns the (excess) kurtosis of a given probability distrbution
MnProbDistLikelihoodReturns the likelihood of a given dataset for a a given probability distribution
MnProbDistLogLikelihoodReturns the log-likelihood of a given dataset for a a given probability distribution
MnProbDistMeanReturns the mean of a given probability distrbution
MnProbDistMLEReturns the maximum likelihood estimation vector for parameters of a given probability distribution for a given dataset
MnProbDistMLERestrictedReturns the maximum likelihood estimation vector for parameters (only some of which may vary) of a given probability distribution for a given dataset
MnProbDistPageReturns the main Nematrian web page referring to a given probability distribution
MnProbDistParamCountReturns the number of the parameters used in the specification of the probability distribution
MnProbDistParamNamesReturns the names of the parameters used in the specification of the probability distribution
MnProbDistPdfEvaluates the probability density function for a given (continuous) probability distribution
MnProbDistPlotCdfReturns a SmartCode for a plot of the cumulative density function of a statistical distribution
MnProbDistPlotCdfsReturns a SmartCode for a plot of the cumulative density function of several statistical distributions
MnProbDistPlotPdfReturns a SmartCode for a plot of the probability density function of a continuous statistical distribution
MnProbDistPlotPdfsReturns a SmartCode for a plot of the probability density function of several continuous statistical distributions
MnProbDistPlotPmfReturns a SmartCode for a plot of the probability mass function of a discrete statistical distribution
MnProbDistPlotPmfsReturns a SmartCode for a plot of the probability mass function of several discrete statistical distributions
MnProbDistPlotQQReturns a SmartCode for a plot of the quantile-quantile plot of a statistical distribution
MnProbDistPlotQQsReturns a SmartCode for a plot of the quantile-quantile plot of several statistical distributions
MnProbDistPmfEvaluates the probability mass function for a given (discrete) probability distribution
MnProbDistPolyEvalCalculates the expected value of a (possibly bounded) polynomial for a given (continuous) probability distribution
MnProbDistQuantileEvaluates the quantile, i.e. inverse cdf, for a given probability distrbution
MnProbDistRandReturns a single random draw from a given probability distrbution
MnProbDistRandArrayReturns a (seeded) random array of draws from a given probability distrbution
MnProbDistRandArrayEqSpReturns a (seeded) random array of draws from a given probability distrbution, using equally spaced quantiles
MnProbDistSkewReturns the skew (skewness) of a given probability distrbution
MnProbDistStdReturns the standard deviation of a given probability distrbution
MnProbDistTailValueAtRiskReturns the tail value at risk of a given probability distribution
MnProbDistTWLSReturns the tail weighted least squares estimation vector for parameters of a given probability distribution for a given dataset
MnProbDistTWLSRestrictedReturns the tail weighted least squares estimation vector for parameters (only some of which may vary) of a given probability distribution for a given dataset
MnProbDistTWMLEReturns the tail weighted maximum likelihood estimation vector for parameters of a given probability distribution for a given dataset
MnProbDistTWMLERestrictedReturns the tail weighted maximum likelihood estimation vector for parameters (only some of which may vary) of a given probability distribution for a given dataset
MnProbDistValueAtRiskReturns the value at risk of a given probability distribution
MnProbDistVarReturns the variance of a given probability distrbution
MnProbDistWeightedLikelihoodReturns the weighted likelihood of a given dataset for a a given probability distribution
MnProbDistWeightedLogLikelihoodReturns the weighted log-likelihood of a given dataset for a a given probability distribution
MnProbDistWeightedMLEReturns the weighted maximum likelihood estimation vector for parameters of a given probability distribution for a given dataset
MnProbDistWeightedMLERestrictedReturns the weighted maximum likelihood estimation vector for parameters (only some of which may vary) of a given probability distribution for a given dataset
MnRecognisedProbDistsReturns a string array listing probability distributions recognised by website analytics