|
gptkbp:instanceOf
|
gptkb:organization
probability_distribution
|
|
gptkbp:affiliatedWith
|
continuous_distribution
exponential_family
location-scale_family
|
|
gptkbp:alsoKnownAs
|
gptkb:Gaussian_distribution
Gaussian_distribution
|
|
gptkbp:central_limit_theorem
|
limit_distribution
|
|
gptkbp:centralLimitTheorem
|
limit distribution
|
|
gptkbp:characteristic
|
exp(iμt - 0.5σ²t²)
|
|
gptkbp:characteristic_function
|
exp(i*t*mu - 0.5*sigma^2*t^2)
|
|
gptkbp:continuity
|
true
|
|
gptkbp:cumulative_distribution_function
|
0.5*(1 + erf((x-mu)/(sigma*sqrt(2))))
|
|
gptkbp:cumulativeDistributionFunction
|
(1/2)[1 + erf((x-μ)/(σ√2))]
|
|
gptkbp:entropy
|
0.5*ln(2πeσ²)
0.5*ln(2*pi*e*sigma^2)
|
|
gptkbp:first_moment
|
mu
|
|
gptkbp:fourth_moment
|
mu^4 + 6*mu^2*sigma^2 + 3*sigma^4
|
|
gptkbp:hasSpecialCase
|
gptkb:exponential_family
gptkb:location-scale_family
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
normal distribution
|
|
gptkbp:is_limit_of_binomial
|
true
|
|
gptkbp:is_limit_of_poisson
|
true
|
|
gptkbp:is_symmetric
|
true
|
|
gptkbp:is_unimodal
|
true
|
|
gptkbp:isConjugatePriorFor
|
mean of normal distribution
variance of normal distribution
|
|
gptkbp:isEllipticalDistribution
|
true
|
|
gptkbp:isInfinitelyDivisible
|
true
|
|
gptkbp:isMaximumEntropyDistribution
|
true
|
|
gptkbp:isSelfDecomposable
|
true
|
|
gptkbp:isStableDistribution
|
true
|
|
gptkbp:isUnimodal
|
true
|
|
gptkbp:kurtosis
|
3
|
|
gptkbp:limitation
|
gptkb:binomial_distribution_(as_n→∞,_p→0,_np=μ)
Poisson distribution (as λ→∞)
sum of independent random variables (central limit theorem)
|
|
gptkbp:maximum_entropy_distribution
|
true
|
|
gptkbp:maximumLikelihoodEstimator
|
sample mean and sample variance
|
|
gptkbp:meaning
|
μ
mu
|
|
gptkbp:medium
|
μ
mu
|
|
gptkbp:mode
|
μ
mu
|
|
gptkbp:moment_generating_function
|
exp(mu*t + 0.5*sigma^2*t^2)
|
|
gptkbp:momentGeneratingFunction
|
exp(μt + 0.5σ²t²)
|
|
gptkbp:moments
|
all moments exist
|
|
gptkbp:namedAfter
|
gptkb:Carl_Friedrich_Gauss
Carl_Friedrich_Gauss
|
|
gptkbp:parameter
|
mean
standard deviation
variance
mu
sigma
sigma_squared
standard_deviation
|
|
gptkbp:pdf
|
(1/(σ√(2π))) * exp(-0.5*((x-μ)/σ)^2)
|
|
gptkbp:probability_density_function
|
f(x) = (1/(sigma*sqrt(2*pi))) * exp(-(x-mu)^2/(2*sigma^2))
|
|
gptkbp:relatedTo
|
bell_curve
central_limit_theorem
chi_squared_distribution
error_function
log_normal_distribution
student_t_distribution
z_score
|
|
gptkbp:second_moment
|
mu^2 + sigma^2
|
|
gptkbp:shape
|
bell curve
|
|
gptkbp:skewness
|
0
|
|
gptkbp:special_case
|
standard_normal_distribution
|
|
gptkbp:standard_deviation
|
sigma
|
|
gptkbp:standard_normal_cdf
|
Phi(x)
|
|
gptkbp:standard_normal_mean
|
0
|
|
gptkbp:standard_normal_pdf
|
f(x) = (1/sqrt(2*pi)) * exp(-x^2/2)
|
|
gptkbp:standard_normal_standard_deviation
|
1
|
|
gptkbp:standard_normal_variance
|
1
|
|
gptkbp:standardDeviation
|
σ
|
|
gptkbp:standardNormalCdf
|
Φ(x)
|
|
gptkbp:standardNormalMean
|
0
|
|
gptkbp:standardNormalPdf
|
(1/√(2π)) * exp(-0.5x²)
|
|
gptkbp:standardNormalStdDev
|
1
|
|
gptkbp:standardNormalVariance
|
1
|
|
gptkbp:subclassOf
|
gptkb:standard_normal_distribution
|
|
gptkbp:supports
|
(-∞, ∞)
x in (-infinity, infinity)
|
|
gptkbp:symmetry
|
true
|
|
gptkbp:third_moment
|
mu^3 + 3*mu*sigma^2
|
|
gptkbp:usedIn
|
gptkb:machine_learning
gptkb:natural_sciences
gptkb:probability_theory
finance
social sciences
statistics
machine_learning
natural_sciences
|
|
gptkbp:variant
|
σ²
sigma_squared
|
|
gptkbp:bfsParent
|
gptkb:Wiener_process
gptkb:Boost.Random
|
|
gptkbp:bfsLayer
|
3
6
|
