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A Dirichlet-distributed random variable can be seen as a multivariate generalization of a Beta distribution. Dirichlet pdf is the conjugate prior of a multinomial in Bayesian inference. :Parameters: alpha : array parameter of the distribution (k dimension for sample of dimension k). size : array number of samples to draw. $X pprox \prod_{i=1}^{k}{x^{lpha_i-1}_i}$ Uses the following property for computation: for each dimension, draw a random sample y_i from a standard gamma generator of shape alpha_i, then X = rac{1}{\sum_{i=1}^k{y_i}} (y_1, ..., y_n) is Dirichlet distributed. Reference: - David Mc Kay : Information Theory, inference and Learning algorithms, chapter 23. the book is available for free at http://www.inference.phy.cam.ac.uk/mackay/ Multinomial distribution. multinomial(n, pvals, size=None) -> random values pvals is a sequence of probabilities that should sum to 1 (however, the last element is always assumed to account for the remaining probability as long as sum(pvals[:-1]) <= 1). Return an array containing multivariate normally distributed random numbers with specified mean and covariance. multivariate_normal(mean, cov) -> random values multivariate_normal(mean, cov, [m, n, ...]) -> random values mean must be a 1 dimensional array. cov must be a square two dimensional array with the same number of rows and columns as mean has elements. The first form returns a single 1-D array containing a multivariate normal. The second form returns an array of shape (m, n, ..., cov.shape[0]). In this case, output[i,j,...,:] is a 1-D array containing a multivariate normal. Logarithmic series distribution. logseries(p, size=None) Hypergeometric distribution. Consider an urn with ngood "good" balls and nbad "bad" balls. If one were to draw nsample balls from the urn without replacement, then the hypergeometric distribution describes the distribution of "good" balls in the sample. hypergeometric(ngood, nbad, nsample, size=None) Geometric distribution with p being the probability of "success" on an individual trial. geometric(p, size=None) Zipf distribution. zipf(a, size=None) Poisson distribution. poisson(lam=1.0, size=None) -> random values Negative Binomial distribution. negative_binomial(n, p, size=None) -> random values Binomial distribution of n trials and p probability of success. binomial(n, p, size=None) -> random values Triangular distribution starting at left, peaking at mode, and ending at right (left <= mode <= right). triangular(left, mode, right, size=None) Wald (inverse Gaussian) distribution. wald(mean, scale, size=None) Rayleigh distribution. rayleigh(scale=1.0, size=None) Log-normal distribution. Note that the mean parameter is not the mean of this distribution, but the underlying normal distribution. lognormal(mean, sigma) <=> exp(normal(mean, sigma)) lognormal(mean=0.0, sigma=1.0, size=None) Logistic distribution. logistic(loc=0.0, scale=1.0, size=None) Gumbel distribution. gumbel(loc=0.0, scale=1.0, size=None) Laplace distribution. laplace(loc=0.0, scale=1.0, size=None) Power distribution. power(a, size=None) Weibull distribution. weibull(a, size=None) Pareto distribution. pareto(a, size=None) von Mises circular distribution with mode mu and dispersion parameter kappa on [-pi, pi]. vonmises(mu, kappa, size=None) Standard Student's t distribution with df degrees of freedom. standard_t(df, size=None) Standard Cauchy with mode=0. standard_cauchy(size=None) Noncentral Chi^2 distribution. noncentral_chisquare(df, nonc, size=None) -> random values Chi^2 distribution. chisquare(df, size=None) -> random values Noncentral F distribution. noncentral_f(dfnum, dfden, nonc, size=None) -> random values F distribution. f(dfnum, dfden, size=None) -> random values Gamma distribution. gamma(shape, scale=1.0, size=None) -> random values Standard Gamma distribution. standard_gamma(shape, size=None) -> random values Standard exponential distribution (scale=1). standard_exponential(size=None) -> random values Exponential distribution. exponential(scale=1.0, size=None) -> random values Beta distribution over [0, 1]. beta(a, b, size=None) -> random values Normal distribution (mean=loc, stdev=scale). normal(loc=0.0, scale=1.0, size=None) -> random values Standard Normal distribution (mean=0, stdev=1). standard_normal(size=None) -> random values Return random integers x such that low <= x <= high. random_integers(low, high=None, size=None) -> random values. If high is None, then 1 <= x <= low. Returns zero-mean, unit-variance Gaussian random numbers in an array of shape (d0, d1, ..., dn). randn(d0, d1, ..., dn) -> random values Note: This is a convenience function. If you want an interface that takes a tuple as the first argument use numpy.random.standard_normal(shape_tuple). Return an array of the given dimensions which is initialized to random numbers from a uniform distribution in the range [0,1). rand(d0, d1, ..., dn) -> random values Note: This is a convenience function. If you want an interface that takes a tuple as the first argument use numpy.random.random_sample(shape_tuple). Uniform distribution over [low, high). uniform(low=0.0, high=1.0, size=None) -> random values Return random bytes. bytes(length) -> str Return random integers x such that low <= x < high. randint(low, high=None, size=None) -> random values If high is None, then 0 <= x < low. Returns random integers x such that 0 <= x <= sys.maxint. tomaxint(size=None) -> random values Return random floats in the half-open interval [0.0, 1.0). random_sample(size=None) -> random values Set the state from a tuple. state = ('MT19937', int key[624], int pos) set_state(state) Return a tuple representing the internal state of the generator. get_state() -> ('MT19937', int key[624], int pos) Seed the generator. seed(seed=None) seed can be an integer, an array (or other sequence) of integers of any length, or None. If seed is None, then RandomState will try to read data from /dev/urandom (or the Windows analogue) if available or seed from the clock otherwise. fe@fe# fefe#0fefe#Pfefe#`fe@fe#pfefe#fefefeɮfe fefe fefe fefe fefefefefefefefefefe feufe fejfe fe_fe feTfe 0feIfe @fe>fe Pfe3fe `fe(fe pfefe fefe fefe fefe fefe fefe feݭfe feҭfe feɭfe fefe fefe0fefe@fefe Pfefe`fefe pfefefefefe|fe ferfe fekfefedfefe]fefeVfefeOfefeHfefe=fe fe2fe 0fe'fe @fefe Pfefe `fefe pfefe fefe fefe fe֬fe fe̬fe fefe fefe fefe fefe fefe 0fefe@feufe Pfehfe `feZfepfeSfefeMfefeGfefe@fefe:fefe4fefe-fefe'fefe!fefefefefe fefe0fefe@fefePfefe `fefe pfefefeܫfefeԫfefe̫fefe«fe fefe fefe fefefefe fefe fewfe 0fe`fe@feXfePfePfe`feHfepfe@fe0fe%fe@fefe%Pfefe#`fefe fefesum(pvals[:-1]) > 1.0numpy.dualmean and cov must have same lengthcov must be 2 dimensional and squaremean must be 1 dimensionalp > 1.0p < 0.0p > 1.0p < 0.0ngood + nbad < nsamplensample < 1nbad < 1ngood < 1ngood + nbad < nsamplensample < 1nbad < 1ngood < 1p > 1.0p < 0.0p > 1.0p < 0.0a <= 1.0a <= 1.0lam < 0lam < 0p > 1p < 0n <= 0p > 1p < 0n <= 0p > 1p < 0n <= 0p > 1p < 0n <= 0left == rightmode > rightleft > modeleft == rightmode > rightleft > modescale <= 0.0mean <= 0.0scale <= 0mean <= 0scale <= 0.0scale <= 0sigma <= 0.0sigma <= 0scale <= 0scale <= 0scale <= 0scale <= 0scale <= 0scale <= 0a <= 0a <= 0a <= 0a <= 0a <= 0a <= 0kappa < 0kappa < 0df <= 0df <= 0nonc < 0df <= 1nonc <= 0df <= 0df <= 0df <= 0nonc < 0dfden <= 0dfnum <= 1nonc < 0dfden <= 0dfnum <= 1dfden <= 0dfnum <= 0scale <= 0shape <= 0scale <= 0shape <= 0scale <= 0shape <= 0shape <= 0shape <= 0scale <= 0scale <= 0b <= 0a <= 0b <= 0a <= 0scale <= 0scale <= 0low >= highstate must be 624 longsalgorithm must be 'MT19937'size is not compatible with inputssize is not compatible with inputssize is not compatible with inputssize is not compatible with inputssize is not compatible with inputssize is not compatible with inputsfefefefefefefefefefefefefe!fe`fe%fefe)fefe0fefe7fefe=fefefefe^fe@feAfe fefefeEfefefefeJfefeNfefeTfefefefefefeZfefefePfefefefefebfefe+fefejfe`fefe@ferfefevfefe~fefe#fe@fefefefepfefefefefe2fefe;fepfefefefefefefefe fegfe0fefefefefezfefefepfefefefe0feyfefefe`feOfe0fe9fepfeTfefefefeZfe fe"fefeEfefefefefefefefefefefePfefefefe@fefefefefefefejfePfefe0fefefefefeSfe fefefefefefefefePfeGfe`fefefeNfefefepfefe@fefefefeDfeDfefefefefefefefefeXfefewfe}fefefeXfefefefefefefeXfefefeXfefefefefefefe%fefe%fefefefefefe%fefefe%fefefe%fefefefefefefefeSfeVfefexfefefexfefefexfefefe#fefefefe#fefefe%fefefefefe%fefefefefefe%fefefeCfeGfefeCfeGfefefeCfeGfefefefegfegfefefe fe)feUUUUUU?llfJ?88C$+K?<ٰj_AAz?SˆB8?5gG`wfemtrand.RandomStateContainer for the Mersenne Twister PRNG. Constructor ----------- RandomState(seed=None): initializes the PRNG with the given seed. See the seed() method for details. Distribution Methods ----------------- RandomState exposes a number of methods for generating random numbers drawn from a variety of probability distributions. In addition to the distribution-specific arguments, each method takes a keyword argument size=None. If size is None, then a single value is generated and returned. If size is an integer, then a 1-D numpy array filled with generated values is returned. If size is a tuple, then a numpy array with that shape is filled and returned. seedget_stateset_state__getstate____setstate____reduce__random_sampletomaxintrandintbytesuniformrandrandnrandom_integersstandard_normalnormalbetaexponentialstandard_exponentialstandard_gammagammafnoncentral_fchisquarenoncentral_chisquarestandard_cauchystandard_tvonmisesparetoweibullpowerlaplacegumbellogisticlognormalrayleighwaldtriangularbinomialnegative_binomialpoissonzipfgeometrichypergeometriclogseriesmultivariate_normalmultinomialdirichletshufflepermutationMT19937TypeErrorValueError__RandomState_ctor_rand_spaddanyappendarangearrayasarraycopydotemptyequalfloat64greaterhasattrintintegerisinstancelenlessless_equallistmultiplynumpyrandomreduceshapesizesqrtsubtractsvdtupletypeuintuint32zerosmtrand.pyxnumpy.pxi__import__OOOOCannot convert %s to %sMissing type objectraise: arg 3 must be a traceback or Noneraising a string exception is deprecatedinstance exception may not have a separate valueunpack sequence of wrong size%s.%s does not appear to be the correct type object%s.%s is not a type objectxOmtrand.RandomState.permutationmtrand.shufflemtrand.RandomState.shufflealphaO|Omtrand.RandomState.dirichlet?npvalslO|Omtrand.RandomState.multinomial?meancovOO|Omtrand.RandomState.multivariate_normalmtrand.discd_array_scmtrand.discd_arraypmtrand.RandomState.logseriesngoodnbadnsampleOOO|Omtrand.RandomState.hypergeometricmtrand.discnmN_array_scmtrand.discnmN_arraymtrand.RandomState.geometricamtrand.RandomState.zipflam|OOmtrand.RandomState.poissonmtrand.discnp_array_scmtrand.discnp_arraymtrand.RandomState.negative_binomialmtrand.RandomState.binomialmtrand.cont3_array_scmtrand.cont3_arrayleftmoderightmtrand.RandomState.triangularmtrand.cont2_array_scmtrand.cont2_arrayscalemtrand.RandomState.waldmtrand.cont1_array_scmtrand.cont1_arraymtrand.RandomState.rayleighsigma|OOOmtrand.RandomState.lognormallocmtrand.RandomState.logisticmtrand.RandomState.gumbelmtrand.RandomState.laplacemtrand.RandomState.powermtrand.RandomState.weibullmtrand.RandomState.paretomukappamtrand.RandomState.vonmisesdfmtrand.RandomState.standard_tmtrand.cont0_array|Omtrand.RandomState.standard_cauchynoncmtrand.RandomState.noncentral_chisquaremtrand.RandomState.chisquaredfnumdfdenmtrand.RandomState.noncentral_fmtrand.RandomState.fO|OOmtrand.RandomState.gammamtrand.RandomState.standard_gammamtrand.RandomState.standard_exponentialmtrand.RandomState.exponentialbmtrand.RandomState.betamtrand.RandomState.normalmtrand.RandomState.standard_normallowhighmtrand.RandomState.random_integersmtrand.RandomState.randnmtrand.RandomState.randmtrand.RandomState.uniformlengthImtrand.RandomState.bytesmtrand.RandomState.randintmtrand.disc0_arraymtrand.RandomState.tomaxintmtrand.RandomState.random_samplemtrand.RandomState.__reduce__statemtrand.RandomState.__setstate__mtrand.RandomState.__getstate__mtrand.RandomState.set_statemtrand.set_statemtrand.RandomState.get_statemtrand.RandomState.seedmtrand.RandomState.__init__mtrand__builtin____builtins__dtypendarrayflatiterbroadcastRandomStatenumpy.core.multiarray_ARRAY_APInumpy.core.multiarray failed to importmodule compiled against version %x of C-API but this version of numpy is %xno errorrandom device unvavailableL%@@???UUUUUU?Am{????(\@ffffff@?.@Ax&?@@ ?UUUUUU? CBCCUFl"H A??A?= ףp=@n?[ m?h|?5333333 @r?$~?@B>٬ @r鷯?Q?Q?9v?? A?:0yE>-DT! @@@?-DT!@????@??@UUUUUU??3?r?q?@@@0@?-LIBGCCW32-EH-3-SJLJ-GTHR-MINGW32w32_sharedptr->size == sizeof(W32_EH_SHARED)../../gcc-3.4.5/gcc/config/i386/w32-shared-ptr.cGetAtomNameA (atom, s, sizeof(s)) != 0wG2(,0=mtrand.pydinitmtrand|DL0d(@Tdt,<Xl|,@Xl$@Tdt(@Pd0Pl| 0DXp  (08@LX`ht|(@Tdt,<Xl|,@Xl$@Tdt(@Pd0Pl| 0DXp  (08@LX`ht|PyArg_ParseTupleAndKeywordsPyCObject_AsVoidPtr$PyCObject_Type0PyClass_Type3PyCode_NewSPyDict_CopyUPyDict_DelItemStringWPyDict_GetItemString\PyDict_New^PyDict_SetItem_PyDict_SetItemStringhPyErr_ClearjPyErr_ExceptionMatcheskPyErr_FetchlPyErr_FormatpPyErr_NormalizeExceptionqPyErr_OccurredrPyErr_PrintuPyErr_RestorePyErr_SetObjectPyErr_SetStringPyErr_WarnExPyErr_WriteUnraisablePyEval_CallObjectWithKeywordsPyExc_DeprecationWarningPyExc_ImportErrorPyExc_NameErrorPyExc_RuntimeErrorPyExc_SystemErrorPyExc_TypeErrorPyExc_ValueErrorPyFloat_AsDoublePyFloat_FromDoublePyFrame_NewPyImport_AddModule PyImport_ImportModulePyInstance_TypePyInt_AsLongPyInt_AsUnsignedLongMaskPyInt_FromLong'PyIter_Next.PyList_New0PyList_SetItemBPyLong_FromUnsignedLongUPyMem_FreeVPyMem_MallocePyModule_GetDictpPyNumber_AddPyNumber_MultiplyPyNumber_SubtractPyObject_CallFunctionPyObject_CallObjectPyObject_CmpPyObject_GetAttrPyObject_GetAttrStringPyObject_GetItemPyObject_GetIterPyObject_IsTruePyObject_SetAttrPyObject_SetAttrStringPyObject_SetItemPySequence_GetSlice2PyString_FromString3PyString_FromStringAndSize4PyString_InternFromString9PyString_TypeLPyThreadState_GetdPyTraceBack_HerefPyTraceBack_TypeiPyTuple_GetSlicejPyTuple_NewmPyTuple_SizenPyTuple_TypeqPyType_IsSubtyperPyType_ReadysPyType_TypePy_InitModule4w_Py_NoneStruct]CryptAcquireContextAnCryptGenRandomxCryptReleaseContextAddAtomAFindAtomAGetAtomNameA8__dllonexit_errno_ftimeRacos]ceil_clock`cosfexpkfflushqfloorrfmodzfreelogmallocmemcpypowsqrto_assertabortzmemsetpython25.dllADVAPI32.DLL(((KERNEL32.dll<<<<<<<<<<<<<<<<<msvcr71.dllPPPmsvcrt.dllC0M0q0000001,1b1l1112)2I2k222$393L3w33333445&595B5N5p5z55'6B6M6v66666666$737Q7f7w777778$8-888Q8^8s888888"909;9\9n999::%:+::};;;;;; <0<9>%>>>1?J?P?[?p?u??????? 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