diff --git a/mathfunctionize/.mathfunctionize.py.swp b/mathfunctionize/.mathfunctionize.py.swp
new file mode 100644
index 0000000..0b901f5
Binary files /dev/null and b/mathfunctionize/.mathfunctionize.py.swp differ
diff --git a/mathfunctionize/mathfunctionize.py b/mathfunctionize/mathfunctionize.py
index 4c72883..2f7b615 100644
--- a/mathfunctionize/mathfunctionize.py
+++ b/mathfunctionize/mathfunctionize.py
@@ -15,6 +15,14 @@ def modulo(a, b):
     return a % b
 def flatDivision(a, b):
     return a // b
+def gamma(x):
+    if x == 0 or (x < 0 and x % 1 == 0):
+        raise Exception("Invalid input")
+    if x == 1:
+        return 1
+    if x == 0.5:
+        return squareRoot(pi)
+    return (x - 1) * gamma(x - 1)
 def factorial(x):
     if x == 0:
         return 1
@@ -53,11 +61,687 @@ def derangements(n):
             continue
         res += (1 / factorial(i))
     return int(factorial(n) * res)
-
 # probability
 def bayes_theorem(priorA, priorB, likelihoodA, likelihoodB):
     return (priorA * likelihoodA) / ((priorA * likelihoodA) + (priorB * likelihoodB))
+def uniformPDF(a, b):
+    return 1 / (b - a)
+def uniformCDF(X, a, b):
+    if X < a:
+        return 0
+    if X > b:
+        return 1
+    return (X - a) / (b - a)
+def normalPDF(X, mean, stdDev):
+    coeff = 1 / (stdDev * ((2 * pi) ** 0.5))
+    exponent = -0.5 * (((X - mean) / stdDev) ** 2)
+    return coeff * (e ** exponent)
+def normalCDF(x, mean, stdDev):
+    z = (x - mean) / stdDev
+    t = 1 / (1 + 0.2316419 * absolute(z))
+    d = 0.3989423 * e ** (-z * z / 2)
+    prob = d * t * (0.3193815 + t * (-0.3565638 + t * (1.781478 + t * (-1.821256 + t * 1.330274))))
+    if z > 0:
+        prob = 1 - prob
+    return prob
+def gammaPDF(x, a, b):
+    return (1/gamma(a))*power((b*x),(a/x))*power(e,(-b*x))
+def chiSquarePDF():
+    pass
+def inverseGammaPDF():
+    pass
+def betaPDF():
+    pass
+def arcsinePDF():
+    pass
+def studentTPDF():
+    pass
+def fDistributionPDF():
+    pass
+def poissonPDF():
+    pass
+def binomialPDF():
+    pass
+def geometricPDF():
+    pass
+def hypergeometricPDF():
+    pass
+def negativeBinomialPDF():
+    pass
+def bernoulliPDF():
+    pass
+def multinomialPDF():
+    pass
+def exponentialPDF():
+    pass
+def weibullPDF():
+    pass
+def cauchyPDF():
+    pass
+def logisticPDF():
+    pass
+def laplacePDF():
+    pass
+def paretoPDF():
+    pass
+def rayleighPDF():
+    pass
+def powerPDF():
+    pass
+def uniformDiscretePDF():
+    pass
+def zipfPDF():
+    pass
+def logNormalPDF():
+    pass
+def gumbelPDF():
+    pass
+def triangularPDF():
+    pass
+def vonMisesPDF():
+    pass
+def levyPDF():
+    pass
+def wignerPDF():
+    pass
+def diracDeltaPDF():
+    pass
+def maxwellBoltzmannPDF():
+    pass
+def inverseGuassianPDF():
+    pass
+def betaPrimePDF():
+    pass
+def kumaraswamyPDF():
+    pass
+def dirchletPDF():
+    pass
+def wishartPDF():
+    pass
+def inverseWishartPDF():
+    pass
+def skewNormalPDF():
+    pass
+def generalizedExtremeValuePDF():
+    pass
+def errorFunctionPDF():
+    pass
+def hyperbolicPDF():
+    pass
+def varianceGammaPDF():
+    pass
+def logLogisticPDF():
+    pass
+def burrPDF():
+    pass
+def frechetPDF():
+    pass
+def generalizedParetoPDF():
+    pass
+def halfNormalPDF():
+    pass
+def halfCauchyPDF():
+    pass
+def halfLogisticPDF():
+    pass
+def halfTDistributionPDF():
+    pass
+def triangularDiscretePDF():
+    pass
+def bernoulliTrialPDF():
+    pass
+def multinoulliPDF():
+    pass
+def categoricalPDF():
+    pass
+def dirichletProcessPDF():
+    pass
+def chineseRestaurantProcessPDF():
+    pass
+def stickBreakingProcessPDF():
+    pass
+def indianBuffetProcessPDF():
+    pass
+def poissonProcessPDF():
+    pass
+def brownianMotionPDF():
+    pass
+def wienerProcessPDF():
+    pass
+def gammaProcessPDF():
+    pass
+def inverseGaussianProcessPDF():
+    pass
+def levyProcessPDF():
+    pass
+def stableProcessPDF():
+    pass
+def fractionalBrownianMotionPDF():
+    pass
+def markovProcessPDF():
+    pass
+def hiddenMarkovModelPDF():
+    pass
+def queuingTheoryPDF():
+    pass
+def renewalProcessPDF():
+    pass
+def birthDeathProcessPDF():
+    pass
+def branchingProcessPDF():
+    pass
+def randomWalkPDF():
+    pass
+def martingalePDF():
+    pass
+def ergodicProcessPDF():
+    pass
+def mixingProcessPDF():
+    pass
+def stationaryProcessPDF():
+    pass
+def nonStationaryProcessPDF():
+    pass
+def timeSeriesAnalysisPDF():
+    pass
+def copulaPDF():
+    pass
+def vineCopulaPDF():
+    pass
+def empiricalDistributionFunctionPDF():
+    pass
+def kernelDensityEstimationPDF():
+    pass
+def monteCarloSimulationPDF():
+    pass
+def bootstrapPDF():
+    pass
+def jackknifePDF():
+    pass
+def crossValidationPDF():
+    pass
+def bayesianInferencePDF():
+    pass
+def frequentistInferencePDF():
+    pass
+def maximumLikelihoodEstimationPDF():
+    pass
+def methodOfMomentsPDF():
+    pass
+def expectationMaximizationPDF():
+    pass
+def variationalInferencePDF():
+    pass
+def gibbsSamplingPDF():
+    pass
+def metropolisHastingsPDF():
+    pass
+def sliceSamplingPDF():
+    pass
+def hamiltonianMonteCarloPDF():
+    pass
+def noUTurnSamplerPDF():
+    pass
+def sequentialMonteCarloPDF():
+    pass
+def particleFilterPDF():
+    pass
+def kalmanFilterPDF():
+    pass
+def extendedKalmanFilterPDF():
+    pass
+def unscentedKalmanFilterPDF():
+    pass
+def ensembleKalmanFilterPDF():
+    pass
+def smoothParticleFilterPDF():
+    pass
+def resamplePDF():
+    pass
+def importanceSamplingPDF():
+    pass
+def rareEventSimulationPDF():
+    pass
+def quasiMonteCarloPDF():
+    pass
+def latinHypercubeSamplingPDF():
+    pass
+def sobolSequencePDF():
+    pass
+def haltonSequencePDF():
+    pass
+def faureSequencePDF():
+    pass
+def niederreiterSequencePDF():
+    pass
+def scrambledSequencePDF():
+    pass
+def randomizedSequencePDF():
+    pass
+def lowDiscrepancySequencePDF():
+    pass
+def highDimensionalIntegrationPDF():
+    pass
+def adaptiveQuadraturePDF():
+    pass
+def gaussianQuadraturePDF():
+    pass
+def monteCarloIntegrationPDF():
+    pass
+def quasiMonteCarloIntegrationPDF():
+    pass
+def sparseGridIntegrationPDF():
+    pass
+def multilevelMonteCarloPDF():
+    pass
+def multilevelQuasiMonteCarloPDF():
+    pass
+def multilevelSparseGridPDF():
+    pass
+def polynomialChaosPDF():
+    pass
+def stochasticCollocationPDF():
+    pass
+def generalizedPolynomialChaosPDF():
+    pass
+def stochasticGalerkinPDF():
+    pass
+def stochasticFiniteElementPDF():
+    pass
+def uncertaintyQuantificationPDF():
+    pass
+def sensitivityAnalysisPDF():
+    pass
+def reliabilityAnalysisPDF():
+    pass
+def riskAnalysisPDF():
+    pass
+def decisionAnalysisPDF():
+    pass
+def gameTheoryPDF():
+    pass
+def auctionTheoryPDF():
+    pass
+def mechanismDesignPDF():
+    pass
+def socialChoiceTheoryPDF():
+    pass
+def votingTheoryPDF():
+    pass
+def matchingTheoryPDF():
+    pass
+def networkTheoryPDF():
+    pass
+def graphTheoryPDF():
+    pass
+def combinatorialOptimizationPDF():
+    pass
+def integerProgrammingPDF():
+    pass
+def linearProgrammingPDF():
+    pass
+def dynamicProgrammingPDF():
+    pass
+def convexOptimizationPDF():
+    pass
+def nonConvexOptimizationPDF():
+    pass
+def globalOptimizationPDF():
+    pass
+def localOptimizationPDF():
+    pass
+def heuristicOptimizationPDF():
+    pass
+def metaheuristicOptimizationPDF():
+    pass
+def evolutionaryAlgorithmPDF():
+    pass
+def geneticAlgorithmPDF():
+    pass
+def particleSwarmOptimizationPDF():
+    pass
+def antColonyOptimizationPDF():
+    pass
+def simulatedAnnealingPDF():
+    pass
+def tabuSearchPDF():
+    pass
+def differentialEvolutionPDF():
+    pass
+def harmonySearchPDF():
+    pass
+def cuckooSearchPDF():
+    pass
+def fireflyAlgorithmPDF():
+    pass
+def batAlgorithmPDF():
+    pass
+def greyWolfOptimizerPDF():
+    pass
+def lionOptimizationAlgorithmPDF():
+    pass
+def whaleOptimizationAlgorithmPDF():
+    pass
+def dragonflyAlgorithmPDF():
+    pass
+def mothFlameOptimizerPDF():
+    pass
+def slimeMouldAlgorithmPDF():
+    pass
+def grasshopperOptimizationAlgorithmPDF():
+    pass
+def elephantHerdingOptimizationPDF():
+    pass
+def krillHerdAlgorithmPDF():
+    pass
+def waterWaveOptimizationPDF():
+    pass
+def sineCosineAlgorithmPDF():
+    pass
+def salpSwarmAlgorithmPDF():
+    pass
+def marinePredatorsAlgorithmPDF():
+    pass
+def arithmeticOptimizationAlgorithmPDF():
+    pass
+def hungerGamesSearchPDF():
+    pass
+def earthwormOptimizationAlgorithmPDF():
+    pass
+def spottedHyenaOptimizerPDF():
+    pass
+def redFoxOptimizerPDF():
+    pass
+def goldenJackalOptimizerPDF():
+    pass
+def socialSpiderAlgorithmPDF():
+    pass
+def coronavirusOptimizationAlgorithmPDF():
+    pass
+# Additional Probability Distributions
+def ricePDF():
+    pass
+def nakagamiPDF():
+    pass
+def chiPDF():  # chi distribution (not chi-square)
+    pass
+def foldedNormalPDF():
+    pass
+def truncatedNormalPDF():
+    pass
+def johnsonSUPDF():
+    pass
+def johnsonSBPDF():
+    pass
+def zeroInflatedPoissonPDF():
+    pass
+def conwayMaxwellPoissonPDF():
+    pass
+def polyaPDF():
+    pass
+def yuleSimonPDF():
+    pass
+def borelPDF():
+    pass
+def discreteWeibullPDF():
+    pass
+def logarithmicSeriesPDF():
+    pass
+def benfordPDF():
+    pass
+def rademacherPDF():
+    pass
+def skellamPDF():
+    pass
+def compoundPoissonPDF():
+    pass
+def mixedPoissonPDF():
+    pass
+def betaBinomialPDF():
+    pass
+def betaNegativeBinomialPDF():
+    pass
+def trapezoidalPDF():
+    pass
+def uQuadraticPDF():
+    pass
+def raisedCosinePDF():
+    pass
+def wignerSemicirclePDF():
+    pass
+def lomaxPDF():
+    pass
+def discreteUniformIntegerPDF():
+    pass
+
+# Additional Stochastic Processes
+def ornsteinUhlenbeckProcessPDF():
+    pass
+def coxIngersollRossProcessPDF():
+    pass
+def vasicekProcessPDF():
+    pass
+def hullWhiteProcessPDF():
+    pass
+def blackScholesProcessPDF():
+    pass
+def hestonProcessPDF():
+    pass
+def jumpDiffusionProcessPDF():
+    pass
+def mertonJumpDiffusionPDF():
+    pass
+def kouJumpDiffusionPDF():
+    pass
+def varianceGammaProcessPDF():
+    pass
+def normalInverseGaussianProcessPDF():
+    pass
+def hyperbolicProcessPDF():
+    pass
+def hawkesProcessPDF():
+    pass
+def coxProcessPDF():
+    pass
+def doublyStochasticPoissonProcessPDF():
+    pass
+def shotNoiseProcessPDF():
+    pass
+def telegraphProcessPDF():
+    pass
+def randomFieldPDF():
+    pass
+def gaussianRandomFieldPDF():
+    pass
+def markovRandomFieldPDF():
+    pass
+
+# Additional Copulas
+def gaussianCopulaPDF():
+    pass
+def tCopulaPDF():
+    pass
+def claytonCopulaPDF():
+    pass
+def gumbelCopulaPDF():
+    pass
+def frankCopulaPDF():
+    pass
+def archimedeanCopulaPDF():
+    pass
+def ellipticalCopulaPDF():
+    pass
+def extremeValueCopulaPDF():
+    pass
+
+# Machine Learning Algorithms
+def supportVectorMachinePDF():
+    pass
+def randomForestPDF():
+    pass
+def gradientBoostingPDF():
+    pass
+def neuralNetworkPDF():
+    pass
+def deepLearningPDF():
+    pass
+def convolutionalNeuralNetworkPDF():
+    pass
+def recurrentNeuralNetworkPDF():
+    pass
+def longShortTermMemoryPDF():
+    pass
+def gatedRecurrentUnitPDF():
+    pass
+def transformerPDF():
+    pass
+def attentionMechanismPDF():
+    pass
+def variationalAutoencoderPDF():
+    pass
+def generativeAdversarialNetworkPDF():
+    pass
+def reinforcementLearningPDF():
+    pass
+def qLearningPDF():
+    pass
+def deepQLearningPDF():
+    pass
+def policyGradientPDF():
+    pass
+def actorCriticPDF():
+    pass
+
+# Additional Optimization Algorithms
+def beeColonyOptimizationPDF():
+    pass
+def artificialBeeColonyPDF():
+    pass
+def honeyBeeOptimizationPDF():
+    pass
+def bumblebeeOptimizationPDF():
+    pass
+def flowerPollinationAlgorithmPDF():
+    pass
+def butterflyOptimizationAlgorithmPDF():
+    pass
+def birdSwarmAlgorithmPDF():
+    pass
+def fishSchoolSearchPDF():
+    pass
+def catSwarmOptimizationPDF():
+    pass
+def pigeonInspiredOptimizationPDF():
+    pass
+def cockroachSwarmOptimizationPDF():
+    pass
+def monkeySearchAlgorithmPDF():
+    pass
+def bearOptimizationAlgorithmPDF():
+    pass
+def cheetahOptimizerPDF():
+    pass
+def jaguarAlgorithmPDF():
+    pass
+def leopardOptimizationAlgorithmPDF():
+    pass
+def tigerOptimizationAlgorithmPDF():
+    pass
+def pantherOptimizationAlgorithmPDF():
+    pass
+def lionessOptimizationAlgorithmPDF():
+    pass
+def zebbraOptimizationAlgorithmPDF():
+    pass
+def giraffeOptimizationAlgorithmPDF():
+    pass
+def rhinoOptimizationAlgorithmPDF():
+    pass
+def hippoOptimizationAlgorithmPDF():
+    pass
+def crocodileOptimizationAlgorithmPDF():
+    pass
+def turtleOptimizationAlgorithmPDF():
+    pass
+def snakeOptimizationAlgorithmPDF():
+    pass
+def lizardOptimizationAlgorithmPDF():
+    pass
+def geckoOptimizationAlgorithmPDF():
+    pass
+def chameleonOptimizationAlgorithmPDF():
+    pass
+def frogLeapingAlgorithmPDF():
+    pass
+def shuffledFrogLeapingAlgorithmPDF():
+    pass
+def dolphinEcholocationAlgorithmPDF():
+    pass
+def sharkOptimizationAlgorithmPDF():
+    pass
+def fishSwarmOptimizationPDF():
+    pass
+def schoolingFishOptimizationPDF():
+    pass
+def jellyfishSearchOptimizationPDF():
+    pass
+def seagullOptimizationAlgorithmPDF():
+    pass
+def pelicanOptimizationAlgorithmPDF():
+    pass
+def spiderMonkeyOptimizationPDF():
+    pass
+def orangutanOptimizationAlgorithmPDF():
+    pass
+def chimpanzeeOptimizationAlgorithmPDF():
+    pass
+def baboonOptimizationAlgorithmPDF():
+    pass
+def gorillaOptimizationAlgorithmPDF():
+    pass
 
+# Physics-Based Optimization
+def simulatedAnnealingPDF():
+    pass
+def gravitationalSearchAlgorithmPDF():
+    pass
+def bigBangBigCrunchPDF():
+    pass
+def blackHoleAlgorithmPDF():
+    pass
+def galaxyBasedSearchAlgorithmPDF():
+    pass
+def centralForceOptimizationPDF():
+    pass
+def artificialPhysicsOptimizationPDF():
+    pass
+def atomicSearchOptimizationPDF():
+    pass
+def nuclearReactionOptimizationPDF():
+    pass
+def quantumBehavioredParticleSwarmPDF():
+    pass
+# Human-Based Optimization
+def teachingLearningBasedOptimizationPDF():
+    pass
+def socioEvolutionLearningOptimizationPDF():
+    pass
+def brainstormOptimizationPDF():
+    pass
+def culturalAlgorithmPDF():
+    pass
+def imperialistCompetitiveAlgorithmPDF():
+    pass
+def leagueChampionshipAlgorithmPDF():
+    pass
+def volleyballPremierLeaguePDF():
+    pass
+def soccerrLeagueCompetitionPDF():
+    pass
+def baseballOptimizationAlgorithmPDF():
+    pass
+def goldenBallAlgorithmPDF():
+    pass
 #complex numbers
 def complex_addition(a, b):
     if a.find("+") != -1:
diff --git a/test_.py b/test_.py
index b1ffdae..f813c52 100644
--- a/test_.py
+++ b/test_.py
@@ -1,9 +1,7 @@
 import unittest
 import sys
 import os
-
 from mathfunctionize import mathfunctionize
-
 class TestCounting(unittest.TestCase):
     def test_permutations(self):
         self.assertEqual(mathfunctionize.permutations(5, 3), 60)
@@ -17,6 +15,12 @@ def test_derangements(self):
 
     def test_combinations(self):
         self.assertEqual(mathfunctionize.combinations(5, 3), 10)
+    def test_gamma(self):
+        self.assertEqual(mathfunctionize.gamma(5), 24)
+        self.assertAlmostEqual(mathfunctionize.gamma(5.5), 52.34277778455352, places=5)
+        self.assertAlmostEqual(mathfunctionize.gamma(.5), 1.7724538509055159, places=5)
+        self.assertAlmostEqual(mathfunctionize.gamma(1.5), 0.8862269254527579, places=5)
+        self.assertAlmostEqual(mathfunctionize.gamma(2.5), 1.329340388179137, places=5)
 
 class TestArithmetic(unittest.TestCase):
     def test_addition(self):