Statistics

Full name SMRUCC.genomics.Analysis.HTS.FELLA.Math.Statistics Assembly SMRUCC.genomics.Analysis.HTS.FELLA Members 28

Statistical utility functions required for FELLA enrichment analysis. All implementations use only basic .NET math functions (System.Math).

01 Syntax

SMRUCC.genomics.Analysis.HTS.FELLA.Math.Statistics

02 Methods

Name	Overloads	Summary
NormalCDF	1	Standard normal CDF: P(Z <= x) using Abramowitz & Stegun approximation.
NormalInverseCDF	1	Inverse of the standard normal CDF (quantile function).
ZScore	1	Compute z-score from observed value, mean, and standard deviation.
PScoreFromZScore	1	Compute p-score from z-score using normal CDF.
StudentTCDF	1	Student's t-distribution CDF using regularized incomplete beta function.
PScoreFromT	1	Compute p-score using Student's t approximation.
PScoreFromGamma	1	Compute p-score using Gamma approximation.
GammaCDF	1	Gamma distribution CDF using regularized incomplete gamma function.
LogGamma	1	Log of the Gamma function using Lanczos approximation.
GammaFunc	1	Gamma function using Lanczos approximation.
RegularizedIncompleteGamma	1	Regularized lower incomplete gamma function P(a, x) = gamma(a,x)/Gamma(a).
GammaSeries	1	Series expansion for the regularized lower incomplete gamma function.
GammaContinuedFraction	1	Continued fraction representation for the upper incomplete gamma function.
LogBeta	1	Log of the Beta function.
BetaFunc	1	Beta function B(a,b).
RegularizedIncompleteBeta	1	Regularized incomplete beta function I_x(a,b).
LogBinomial	1	Log of the binomial coefficient: log(C(n,k))
HypergeometricPMF	1	Hypergeometric PMF: P(X = k) where X ~ Hypergeometric(M, n, N) M = population size (total compounds in background) n = number of success states in population (compounds in pathwa…
HypergeometricCDF	1	Hypergeometric CDF: P(X <= k) where X ~ Hypergeometric(M, n, N) Used for over-representation analysis (one-tailed test).
HypergeometricPValue	1	Hypergeometric test p-value (one-tailed, upper tail).
BenjaminiHochberg	1	Benjamini-Hochberg procedure for FDR control.
RandomPermutation	1	Generate a random permutation of integers 0 to n-1 using Fisher-Yates shuffle.
RandomSample	1	Randomly select k items from a population of n items.
EmpiricalPValue	1	Compute empirical p-value from Monte Carlo simulation.
Mean	1	Compute mean of a double array.
Variance	1	Compute variance of a double array (sample variance with Bessel's correction).
StdDev	1	Compute standard deviation.
ComputeMeanVariance	1	Compute mean and variance in a single pass.

03 Members

method NormalCDF #

NormalCDF(Double)

Standard normal CDF: P(Z <= x) using Abramowitz & Stegun approximation. Maximum absolute error: 7.5e-8

method NormalInverseCDF #

NormalInverseCDF(Double)

Inverse of the standard normal CDF (quantile function). Uses rational approximation by Peter Acklam.

method ZScore #

ZScore(Double, Double, Double)

Compute z-score from observed value, mean, and standard deviation.

method PScoreFromZScore #

PScoreFromZScore(Double)

Compute p-score from z-score using normal CDF. In FELLA, p-score = Phi(z) where z = (score - mu) / sigma. Lower p-scores indicate more significant nodes.

method StudentTCDF #

StudentTCDF(Double, Double)

Student's t-distribution CDF using regularized incomplete beta function. P(T <= t) with df degrees of freedom.

method PScoreFromT #

PScoreFromT(Double, Double)

Compute p-score using Student's t approximation.

method PScoreFromGamma #

PScoreFromGamma(Double, Double, Double)

Compute p-score using Gamma approximation. Shape = E^2/V, Scale = V/E, then p-score = GammaCDF(score; shape, scale).

method GammaCDF #

GammaCDF(Double, Double, Double)

Gamma distribution CDF using regularized incomplete gamma function.

method LogGamma #

LogGamma(Double)

Log of the Gamma function using Lanczos approximation.

method GammaFunc #

GammaFunc(Double)

Gamma function using Lanczos approximation.

method RegularizedIncompleteGamma #

RegularizedIncompleteGamma(Double, Double)

Regularized lower incomplete gamma function P(a, x) = gamma(a,x)/Gamma(a). Uses series expansion and continued fraction representation.

method GammaSeries #

GammaSeries(Double, Double)

Series expansion for the regularized lower incomplete gamma function.

method GammaContinuedFraction #

GammaContinuedFraction(Double, Double)

Continued fraction representation for the upper incomplete gamma function. Returns Q(a,x) = 1 - P(a,x). Uses modified Lentz's method.

method LogBeta #

LogBeta(Double, Double)

Log of the Beta function.

method BetaFunc #

BetaFunc(Double, Double)

Beta function B(a,b).

method RegularizedIncompleteBeta #

RegularizedIncompleteBeta(Double, Double, Double)

Regularized incomplete beta function I_x(a,b). Uses continued fraction representation.

method LogBinomial #

LogBinomial(Int32, Int32)

Log of the binomial coefficient: log(C(n,k))

method HypergeometricPMF #

HypergeometricPMF(Int32, Int32, Int32, Int32)

Hypergeometric PMF: P(X = k) where X ~ Hypergeometric(M, n, N) M = population size (total compounds in background) n = number of success states in population (compounds in pathway) N = number of draws (input compounds) k = number of observed successes (input compounds in pathway)

method HypergeometricCDF #

HypergeometricCDF(Int32, Int32, Int32, Int32)

Hypergeometric CDF: P(X <= k) where X ~ Hypergeometric(M, n, N) Used for over-representation analysis (one-tailed test).

method HypergeometricPValue #

HypergeometricPValue(Int32, Int32, Int32, Int32)

Hypergeometric test p-value (one-tailed, upper tail). Tests whether the overlap between input compounds and a pathway is greater than expected by chance. p-value = P(X >= k) = 1 - P(X <= k-1)

method BenjaminiHochberg #

BenjaminiHochberg(Double())

Benjamini-Hochberg procedure for FDR control. Returns adjusted p-values.

method RandomPermutation #

RandomPermutation(Int32, Random)

Generate a random permutation of integers 0 to n-1 using Fisher-Yates shuffle.

method RandomSample #

RandomSample(Int32, Int32, Random)

Randomly select k items from a population of n items. Returns the indices of selected items.

method EmpiricalPValue #

EmpiricalPValue(Double, Double())

Compute empirical p-value from Monte Carlo simulation. p = (count_ge + 1) / (niter + 1) where count_ge is the number of trials with score >= observed.

method Mean #

Mean(Double())

Compute mean of a double array.

method Variance #

Variance(Double())

Compute variance of a double array (sample variance with Bessel's correction).

method StdDev #

StdDev(Double())

Compute standard deviation.

method ComputeMeanVariance #

ComputeMeanVariance(Double(), Double, Double)

Compute mean and variance in a single pass.