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Guide prob dist SSJ User ? s Guide Package probdist Probability Distributions Version September This package provides tools to compute densities mass functions distribution functions and their inverses and reliability functions for various continuous and

SSJ User ? s Guide Package probdist Probability Distributions Version September This package provides tools to compute densities mass functions distribution functions and their inverses and reliability functions for various continuous and discrete probability distributions It also o ?ers facilities for estimating the parameters of some distributions from a data set CSeptember CONTENTS i Contents Overview General Classes Distribution DiscreteDistributionInt ContinuousDistribution DistributionFactory InverseDistFromDensity Discrete Distributions over Integers BernoulliDist BinomialDist GeometricDist HypergeometricDist LogarithmicDist NegativeBinomialDist PascalDist PoissonDist UniformIntDist ConstantIntDist Discrete Distributions over Real Numbers DiscreteDistribution ConstantDist EmpiricalDist CSeptember CONTENTS ii Continuous Distributions BetaDist BetaSymmetricalDist CauchyDist ChiDist ChiSquareDist ChiSquareDistQuick ChiSquareNoncentralDist ErlangDist ExponentialDist ExponentialDistFromMean ExtremeValueDist FatigueLifeDist FisherFDist FoldedNormalDist FrechetDist GammaDist GammaDistFromMoments GumbelDist HalfNormalDist HyperbolicSecantDist HypoExponentialDist HypoExponentialDistQuick HypoExponentialDistEqual InverseGammaDist InverseGaussianDist JohnsonSystem JohnsonSLDist JohnsonSBDist JohnsonSUDist LaplaceDist LogisticDist LoglogisticDist CSeptember CONTENTS LognormalDist LognormalDistFromMoments NakagamiDist NormalDist NormalDistQuick NormalInverseGaussianDist ParetoDist Pearson Dist Pearson Dist PiecewiseLinearEmpiricalDist PowerDist RayleighDist StudentDist StudentDistQuick TriangularDist UniformDist WeibullDist TruncatedDist Empirical Distribution Functions EDF AndersonDarlingDist AndersonDarlingDistQuick CramerVonMisesDist KolmogorovSmirnovPlusDist KolmogorovSmirnovDist KolmogorovSmirnovDistQuick WatsonGDist WatsonUDist CSeptember CONTENTS Overview This package contains a set of Java classes providing methods to compute mass density distribution complementary distribution and inverse distribution functions for some discrete and continuous probability distributions It also provides methods to estimate the parameters of some distributions from empirical data It does not generate random variates for that see the package randvar It is possible to plot the density or the cumulative probabilities of a distribution function either on screen or in a LATEX ?le but for this one has to use the package charts Distributions We recall that the distribution function of a continuous random variable X with density f over the real line is x F x P X ? x f s ds ?? ? while that of a discrete random variable X with mass function p over a ?xed set of real numbers x x x is F x P X ? x p xi xi ? x where p xi P X xi For a discrete distribution over the set of integers one has x F x P X ? x p s s ?? ? where p s P X s We de ?ne F the complementary distribution function of X by F x P X ? x With this de ?nition of F one has F x ?? F x for continuous distributions and F x ?? F x ?? for discrete distributions over the integers This de ?nition is non-standard for the discrete case we have F x P X ? x instead of F x P X x ?? F x We ?nd it more convenient especially for computing p-values in goodness-of- ?t tests The inverse distribution function is de ?ned as F ?? u inf x ?? R F x ? u for ? u ? This function F ?? is often used among other things to generate the random variable X by inversion by passing a U random variate as the value of u The package probdist o ?ers two types of tools for computing p f F