Revision #611 → #1430 · back to history
addedNormal distribution20774e57c3c1
addedCentral limit theorem (informal)180072830861
addedLinear combination of normals is normalcf6d5f477a93
addedStandard normal distribution1209f7fb0984
addedGauss's standard normalae9775e5c3ec
addedStigler's standard normalb9270240d650
addedScaling/shifting standard normal yields general normal2e560b76e9ad
addedStandardization of a normal variatef7df6a5a5d98
addedNotation for normal distribution90296993e5b3
addedPrecision parameterizationdee38998bc1f
addedAlternative precision (reciprocal of standard deviation)2e7d5f6593ee
addedNormal as exponential family4a5c80cf5e8c
addedStandard normal CDF6dec3e90f695
addedError function021da2ebe2ee
addedRelation between Phi and erf36e4357c7547
addedGeneral normal CDFf94353e85339
addedProbability of interval8dfebded381a
addedQ-functiondc985af4ffed
addedRotational symmetry of Phi4978d8a3317f
addedAsymptotic expansion of CDF687d2cdef260
addedTaylor series for normal density1303e3a5648c
addedTaylor series for CDF7502e2834e98
addedRecursive Taylor expansion via Hermite polynomials23147b045e53
added68-95-99.7 rule8071571d7450
addedQuantile/probit function955c5e4f7d71
addedNewton's method for quantilea1cc565c8b06
addedMaximum entropy characterization of normalca2be0e783c7
addedGeary's characterizationc6890e6ac168
addedSymmetries and derivatives of normal density0d83ddce2174
addedProperties of standard normal density6f14e0e7745e
addedPlain and absolute momentsecbe94bcfb0f
addedCentral moments of normalab37b9999642
addedCentral absolute momentsa3ab74b28647
addedConditional expectation on an interval (inverse Mills ratio)2dd06fbc1252
addedFourier transform of normal densityaf2059f6bb7d
addedCharacteristic functiona8ae6eb63104
addedMoment generating function of normal87c33139eb44
addedCumulant generating function5b94777b6a1d
addedStein operator and classf9448f64e851
addedZero-variance limit (Dirac delta)414d89be61a8
addedMaximum entropy theorem for normal531703f9b1ca
addedMarcinkiewicz theorem8b378c2d0edc
addedJointly normal and uncorrelated implies independent13422bb21e20
addedKullback-Leibler divergence of normals37d02de1e96d
addedFisher information matrix2c2557361bc4
addedConjugate prior for the mean5906b7add1ec
addedCentral limit theorem45e60730d645
addedBerry-Esseen theorem1d064dac00eb
addedClosure of normal family under linear transformations75f6b4ccbf26
addedExponential of normal is log-normala8ecdf3f6f41
addedSigmoid of normal is logit-normal48f5b1a6694c
addedAbsolute value: folded/half-normal9dd60c5646e1
addedAbsolute normalized residuals: chi distribution34114e98d110
addedSquare has noncentral chi-squared distribution04e3ddd08aba
addedTruncated normal distribution43ea778286f7
addedSum of independent normals is normal18b30d96748c
addedPolarization identity for normals06f42c85093a
addedStability of normal distributionae4bed9155e0
addedRatio of independent standard normals: Cauchy2450ce1b5ee0
addedEuclidean norm: Rayleigh distributionce3619690d7d
addedLinear combination of independent normals is normal093712a0d995
addedSum of squares: chi-squareda1d987b30b02
addedSample mean and variance independence; t-distribution4bae1bb0bc77
addedF-distribution ratio2e4f2a28635a
addedQuadratic form: generalized chi-squareb0bdb5ee0700
addedSplit normal distribution1ccef187cacd
addedInfinite divisibility of normal9c235ba9e770
addedCramér's decomposition theorem57fadd9c19e2
addedKac-Bernstein theorem1c71d29051c4
addedGeneralized Kac-Bernstein9316eb2cb6ef
addedMultivariate normal distribution6cc559beb971
addedRectified Gaussian distribution7a6d6e7affb0
addedComplex normal distribution0f097e74d115
addedMatrix normal distributiond29c6284f760
addedGaussian processesad0f86491f79
addedGaussian q-distributione2b9d8b55ee6
addedq-Gaussianb20171d7a6d8
addedKaniadakis kappa-Gaussian4a2727785feb
addedTwo-piece normal distributione41414feceae
addedMaximum likelihood estimatorscb79cc5c9232
addedSample meanf14574784b8d
addedLehmann-Scheffé UMVU for sample mean4f25a1406b9c
addedSample variance and Bessel's correction63a893ae97b8
addedCochran's theorem (normal sample mean/variance independence)a3a3472445c1
addedConfidence intervals via t and chi-squarede5d71c2e6a80
addedNormality tests5b6b5be0d9b6
addedQ-Q plot2b3c1d26056f
addedP-P plot7c6e2009d566
addedSum of two quadratics formulaa64d2d99458a
addedBayesian update with known variance2b6151f71514
addedBayesian update with known mean2fdeeee38527
addedBayesian update with unknown mean and varianceb5cac19776b1
addedVelocity distribution of elastic spheres2cb711f5659d
addedQuantum harmonic oscillator ground state56f15cfb77e6
addedDiffusion of a particlecff889cd46f3
addedLog-normality in biology5a9fdf28caf0
addedBlack-Scholes model258aab0bba10
addedMeasurement errors modeled normally9b7fc3155ea6
addedStandardized testing (SAT, IQ)3947ac64d4d8
addedHydrology rainfall/discharge1a365b7bbe10
addedProbability integral transformee83b2f293ea
addedCLT-based 12-uniforms approximation72aa18f5cf70
addedBox-Muller methodb74241bf5ca7
addedMarsaglia polar method3c388bc88f87
addedRatio method7ccdc5541710
addedZiggurat algorithm12a1c61b2ee1
addedZelen & Severo approximation851abb093c4d
addedHart's rational approximationsad977dfddd46
addedMarsaglia Taylor-series algorithm3fdd36803276
addedShore's approximationfc20abc5beeb
addedDe Moivre's binomial expansion resultd334ded97dfc
addedGauss's normal law of errorsea0970373945
addedLaplace's central limit theorem16b9dae3f673