Mathematical functions related to statistics.
This package provides a collection of mathematical constants and numerical functions for statistical computing.
twoπ, # 2π
fourπ, # 4π
halfπ, # π / 2
quartπ, # π / 4
invπ, # 1 / π
twoinvπ, # 2 / π
fourinvπ, # 4 / π
inv2π, # 1 / (2π)
inv4π, # 1 / (4π)
sqrt2, # √2
sqrt3, # √3
sqrtπ, # √π
sqrt2π, # √2π
sqrt4π, # √4π
sqrthalfπ, # √(π / 2)
invsqrt2, # 1 / √2
invsqrt2π, # 1 / √2π
loghalf, # log(1 / 2)
logtwo, # log(2)
logπ, # log(π)
log2π, # log(2π)
log4π, # log(4π)# basicfuns
xlogx, # x * log(x), or 0 when x is zero
xlogy, # x * log(y), or 0 when x is zero
xlog1py, # x * log(1 + y) for x > 0, or 0 when x == 0
logistic, # 1 / (1 + exp(-x))
logit, # log(x / (1 - x))
log1psq, # log(1 + x^2)
log1pexp, # log(1 + exp(x))
log1mexp, # log(1 - exp(x))
log2mexp, # log(2 - exp(x))
logexpm1, # log(exp(x) - 1)
softplus, # alias of log1pexp
invsoftplus, # alias of logexpm1
log1pmx, # log(1 + x) - x
logmxp1, # log(x) - x + 1
logaddexp, # log(exp(x) + exp(y))
logsubexp, # log(abs(exp(x) - exp(y)))
logsumexp, # log(sum(exp(x)))
softmax, # exp(x_i) / sum(exp(x)), for i
softmax!, # inplace softmax
# misc
logmvgamma, # logarithm of multivariate gamma function
lstirling_asymDo note that this package only provides low-level distribution functions. We recommend using the Distributions.jl package for a more convenient interface.
# distrs/beta
betapdf, # pdf of beta distribution
betalogpdf, # logpdf of beta distribution
betacdf, # cdf of beta distribution
betaccdf, # ccdf of beta distribution
betalogcdf, # logcdf of beta distribution
betalogccdf, # logccdf of beta distribution
betainvcdf, # inverse-cdf of beta distribution
betainvccdf, # inverse-ccdf of beta distribution
betainvlogcdf, # inverse-logcdf of beta distribution
betainvlogccdf, # inverse-logccdf of beta distribution
# distrs/binom
binompdf, # pdf of binomial distribution
binomlogpdf, # logpdf of binomial distribution
binomcdf, # cdf of binomial distribution
binomccdf, # ccdf of binomial distribution
binomlogcdf, # logcdf of binomial distribution
binomlogccdf, # logccdf of binomial distribution
binominvcdf, # inverse-cdf of binomial distribution
binominvccdf, # inverse-ccdf of binomial distribution
binominvlogcdf, # inverse-logcdf of binomial distribution
binominvlogccdf, # inverse-logccdf of binomial distribution
# distrs/chisq
chisqpdf, # pdf of chi-square distribution
chisqlogpdf, # logpdf of chi-square distribution
chisqcdf, # cdf of chi-square distribution
chisqccdf, # ccdf of chi-square distribution
chisqlogcdf, # logcdf of chi-square distribution
chisqlogccdf, # logccdf of chi-square distribution
chisqinvcdf, # inverse-cdf of chi-square distribution
chisqinvccdf, # inverse-ccdf of chi-square distribution
chisqinvlogcdf, # inverse-logcdf of chi-square distribution
chisqinvlogccdf, # inverse-logccdf of chi-square distribution
# distrs/fdist
fdistpdf, # pdf of F distribution
fdistlogpdf, # logpdf of F distribution
fdistcdf, # cdf of F distribution
fdistccdf, # ccdf of F distribution
fdistlogcdf, # logcdf of F distribution
fdistlogccdf, # logccdf of F distribution
fdistinvcdf, # inverse-cdf of F distribution
fdistinvccdf, # inverse-ccdf of F distribution
fdistinvlogcdf, # inverse-logcdf of F distribution
fdistinvlogccdf, # inverse-logccdf of F distribution
# distrs/gamma
gammapdf, # pdf of gamma distribution
gammalogpdf, # logpdf of gamma distribution
gammacdf, # cdf of gamma distribution
gammaccdf, # ccdf of gamma distribution
gammalogcdf, # logcdf of gamma distribution
gammalogccdf, # logccdf of gamma distribution
gammainvcdf, # inverse-cdf of gamma distribution
gammainvccdf, # inverse-ccdf of gamma distribution
gammainvlogcdf, # inverse-logcdf of gamma distribution
gammainvlogccdf, # inverse-logccdf of gamma distribution
# distrs/hyper
hyperpdf, # pdf of hypergeometric distribution
hyperlogpdf, # logpdf of hypergeometric distribution
hypercdf, # cdf of hypergeometric distribution
hyperccdf, # ccdf of hypergeometric distribution
hyperlogcdf, # logcdf of hypergeometric distribution
hyperlogccdf, # logccdf of hypergeometric distribution
hyperinvcdf, # inverse-cdf of hypergeometric distribution
hyperinvccdf, # inverse-ccdf of hypergeometric distribution
hyperinvlogcdf, # inverse-logcdf of hypergeometric distribution
hyperinvlogccdf, # inverse-logccdf of hypergeometric distribution
# distrs/nbeta
nbetapdf, # pdf of noncentral beta distribution
nbetalogpdf, # logpdf of noncentral beta distribution
nbetacdf, # cdf of noncentral beta distribution
nbetaccdf, # ccdf of noncentral beta distribution
nbetalogcdf, # logcdf of noncentral beta distribution
nbetalogccdf, # logccdf of noncentral beta distribution
nbetainvcdf, # inverse-cdf of noncentral beta distribution
nbetainvccdf, # inverse-ccdf of noncentral beta distribution
nbetainvlogcdf, # inverse-logcdf of noncentral beta distribution
nbetainvlogccdf, # inverse-logccdf of noncentral beta distribution
# distrs/nbinom
nbinompdf, # pdf of negative nbinomial distribution
nbinomlogpdf, # logpdf of negative nbinomial distribution
nbinomcdf, # cdf of negative nbinomial distribution
nbinomccdf, # ccdf of negative nbinomial distribution
nbinomlogcdf, # logcdf of negative nbinomial distribution
nbinomlogccdf, # logccdf of negative nbinomial distribution
nbinominvcdf, # inverse-cdf of negative nbinomial distribution
nbinominvccdf, # inverse-ccdf of negative nbinomial distribution
nbinominvlogcdf, # inverse-logcdf of negative nbinomial distribution
nbinominvlogccdf, # inverse-logccdf of negative nbinomial distribution
# distrs/nchisq
nchisqpdf, # pdf of noncentral chi-square distribution
nchisqlogpdf, # logpdf of noncentral chi-square distribution
nchisqcdf, # cdf of noncentral chi-square distribution
nchisqccdf, # ccdf of noncentral chi-square distribution
nchisqlogcdf, # logcdf of noncentral chi-square distribution
nchisqlogccdf, # logccdf of noncentral chi-square distribution
nchisqinvcdf, # inverse-cdf of noncentral chi-square distribution
nchisqinvccdf, # inverse-ccdf of noncentral chi-square distribution
nchisqinvlogcdf, # inverse-logcdf of noncentral chi-square distribution
nchisqinvlogccdf, # inverse-logccdf of noncentral chi-square distribution
# distrs/nfdist
nfdistpdf, # pdf of noncentral F distribution
nfdistlogpdf, # logpdf of noncentral F distribution
nfdistcdf, # cdf of noncentral F distribution
nfdistccdf, # ccdf of noncentral F distribution
nfdistlogcdf, # logcdf of noncentral F distribution
nfdistlogccdf, # logccdf of noncentral F distribution
nfdistinvcdf, # inverse-cdf of noncentral F distribution
nfdistinvccdf, # inverse-ccdf of noncentral F distribution
nfdistinvlogcdf, # inverse-logcdf of noncentral F distribution
nfdistinvlogccdf, # inverse-logccdf of noncentral F distribution
# distrs/norm
normpdf, # pdf of normal distribution
normlogpdf, # logpdf of normal distribution
normcdf, # cdf of normal distribution
normccdf, # ccdf of normal distribution
normlogcdf, # logcdf of normal distribution
normlogccdf, # logccdf of normal distribution
norminvcdf, # inverse-cdf of normal distribution
norminvccdf, # inverse-ccdf of normal distribution
norminvlogcdf, # inverse-logcdf of normal distribution
norminvlogccdf, # inverse-logccdf of normal distribution
# distrs/ntdist
ntdistpdf, # pdf of noncentral t distribution
ntdistlogpdf, # logpdf of noncentral t distribution
ntdistcdf, # cdf of noncentral t distribution
ntdistccdf, # ccdf of noncentral t distribution
ntdistlogcdf, # logcdf of noncentral t distribution
ntdistlogccdf, # logccdf of noncentral t distribution
ntdistinvcdf, # inverse-cdf of noncentral t distribution
ntdistinvccdf, # inverse-ccdf of noncentral t distribution
ntdistinvlogcdf, # inverse-logcdf of noncentral t distribution
ntdistinvlogccdf, # inverse-logccdf of noncentral t distribution
# distrs/pois
poispdf, # pdf of Poisson distribution
poislogpdf, # logpdf of Poisson distribution
poiscdf, # cdf of Poisson distribution
poisccdf, # ccdf of Poisson distribution
poislogcdf, # logcdf of Poisson distribution
poislogccdf, # logccdf of Poisson distribution
poisinvcdf, # inverse-cdf of Poisson distribution
poisinvccdf, # inverse-ccdf of Poisson distribution
poisinvlogcdf, # inverse-logcdf of Poisson distribution
poisinvlogccdf, # inverse-logccdf of Poisson distribution
# distrs/tdist
tdistpdf, # pdf of student's t distribution
tdistlogpdf, # logpdf of student's t distribution
tdistcdf, # cdf of student's t distribution
tdistccdf, # ccdf of student's t distribution
tdistlogcdf, # logcdf of student's t distribution
tdistlogccdf, # logccdf of student's t distribution
tdistinvcdf, # inverse-cdf of student's t distribution
tdistinvccdf, # inverse-ccdf of student's t distribution
tdistinvlogcdf, # inverse-logcdf of student's t distribution
tdistinvlogccdf, # inverse-logccdf of student's t distributionAll of the code for this package is released under the MIT/Expat license, but this package depends upon the Rmath.jl package, which currently links to a GPL-licensed library. As such, the package currently constitutes a derived work. Work is underway to remove that dependency.