The Pareto distribution is a heavy-tailed distribution which has applications in network traffic modeling.
MATLAB: Are there functions for calculating the PDF and CDF of the Pareto distribution in the Statistics Toolbox
cdfdistributionparetoparetocdfparetopdfparetorndpdfStatistics and Machine Learning Toolboxstats
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Assuming that a univariate mixture of Gaussians is required (otherwise the inverse cumulative density function (CDF) does not exist), compute the CDF over a grid of, say, 1000 values, and compute the inverse CDF by reverse interpolation.
There is an example of this idea in the demo "Nonparametric Estimates of Cumulative Distribution Functions and Their Inverses" that ships with Statistics Toolbox, but which is not in the web documentation yet. That demo does this in a slightly different context, but the idea carries over.
doc normcdfdoc normpdfWhen you know what you want but not sure the name, try something like
>> lookfor normalrealmin - Smallest positive normalized floating point number.randn - Normally distributed pseudorandom numbers.sprandn - Sparse normally distributed random matrix.surfnorm - Surface normals.isonormals - Isosurface normals.cde - cd elliptic function with normalized complex argument.sne - sn elliptic function with normalized complex argument.addfreqcsmenu - Add a cs menu to switch between linear and normalized frequencyconvertfrequnits - converts between Normalized, Hz, kHz, etchistfit - Histogram with superimposed fitted normal density.jbtest - Jarque-Bera hypothesis test of composite normality.lhsnorm - Generate a latin hypercube sample with a normal distributionlogncdf - Lognormal cumulative distribution function (cdf).lognfit - Parameter estimates and confidence intervals for lognormal data.logninv - Inverse of the lognormal cumulative distribution function (cdf).lognlike - Negative log-likelihood for the lognormal distribution.lognpdf - Lognormal probability density function (pdf).lognrnd - Random arrays from the lognormal distribution.lognstat - Mean and variance for the lognormal distribution.mvncdf - Multivariate normal cumulative distribution function (cdf).mvnpdf - Multivariate normal probability density function (pdf).mvnrnd - Random vectors from the multivariate normal distribution.normcdf - Normal cumulative distribution function (cdf).normfit - Parameter estimates and confidence intervals for normal data.norminv - Inverse of the normal cumulative distribution function (cdf).normlike - Negative log-likelihood for the normal distribution.normpdf - Normal probability density function (pdf).normplot - Displays a normal probability plot.normrnd - Random arrays from the normal distribution.normspec - Plots normal density between specification limits.normstat - Mean and variance for the normal distribution.logn3fit - Fit a 3-param lognormal dist'n using cumulative probabilities.wgtnormfit - Fitting example for a weighted normal distribution.wgtnormfit2 - Fitting example for a weighted normal distribution (log(sigma) parameterization).>>Judicious search terms help but seeing the list of things related to "normal" lets you find the two functions of interest (plus a lot more depending upon which toolboxes are available, maybe) that might be of use/interest...
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