| Probability theory |
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| Probability |
prob
prob-joint
prob-marg
prob-cond |
prob-ind
prob-exc |
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| Probability axioms |
prob-ax |
prob-mon
prob-emp
prob-comp
prob-add
prob-exh
prob-exh2 |
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prob-tot |
| Probability mass function |
pmf |
pmf-sumind
pmf-sifct
pmf-sdfct
pmf-invfct |
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| Probability density function |
pdf |
pdf-sumind
pdf-sifct
pdf-sdfct
pdf-invfct
pdf-linfct |
pdf-cdf |
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| Cumulative distribution function |
cdf
cdf-joint |
cdf-sumind
cdf-sifct
cdf-sdfct |
cdf-pmf
cdf-pdf |
cdf-pit
cdf-itm
cdf-dt |
| Quantile function |
qf |
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qf-cdf |
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| Characteristic function |
cf |
cf-fct |
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| Moment-generating function |
mgf |
mgf-fct |
|
mgf-ltt
mgf-lincomb |
| Cumulant-generating function |
cgf |
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| Probability-generating function |
pgf |
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pgf-mean |
pgf-zero
pgf-one |
| Expected value |
mean
mean-samp
mean-rvec
mean-rmat |
mean-nnrvar
mean-nonneg
mean-lin
mean-mono
mean-mult
mean-tr
mean-qf |
|
mean-prodsqr
mean-tot
mean-lotus |
| Variance |
var
var-samp |
var-nonneg
var-const
var-inv
var-scal
var-sum
var-lincomb
var-add |
var-mean |
var-tot |
| Skewness |
skew
skew-samp |
|
skew-mean |
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| Covariance |
cov
cov-samp
covmat
covmat-samp
covmat-cross |
cov-ind
cov-symm
covmat-inv
covmat-scal
covmat-sum
covmat-symm
covmat-psd |
cov-mean
cov-var
cov-corr
covmat-mean
covmat-corrmat |
cov-tot |
| Correlation |
corr
corr-samp
corrmat
corrmat-samp |
corr-range |
corr-z |
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| Median |
med |
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| Mode |
mode |
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| Standard deviation |
std |
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| Full width at half maximum |
fwhm |
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| Minimum |
min |
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| Maximum |
max |
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| Moments |
mom
mom-raw
mom-cent
mom-stand |
momraw-1st
momraw-2nd
momcent-1st
momcent-2nd |
mom-mgf |
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| Information theory |
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| Shannon entropy |
ent
ent-cond
ent-joint
ent-cross |
ent-nonneg
ent-conc
entcross-conv |
|
gibbs-ineq
logsum-ineq |
| Differential entropy |
dent
dent-cond
dent-joint
dent-cross |
dent-neg
dent-inv
dent-add
dent-addvec
dent-noninv |
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| Discrete mutual information |
mi |
|
dmi-mce
dmi-mje
dmi-jce |
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| Continuous mutual information |
mi |
|
cmi-mcde
cmi-mjde
cmi-jcde |
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| Kullback-Leibler divergence |
kl |
kl-nonneg
kl-nonsymm
kl-conv
kl-add
kl-inv |
kl-ent
kl-dent |
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| Estimation theory |
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| Mean squared error |
mse |
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mse-bnv |
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| Confidence interval |
ci |
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ci-wilks |
| Frequentist statistics |
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| Likelihood theory |
lf
llf
mle
mll |
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|
mle-bias |
| Statistical hypotheses |
hyp
hyp-simp
hyp-point
hyp-tail |
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| Hypothesis testing |
test
h0
h1
test-tail
tstat
size
power
alpha
cval
pval |
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|
pval-h0 |
| Bayesian statistics |
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| Probabilistic modeling |
gm
lf
prior
fpm
jl
post
map
ml |
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jl-lfnprior
post-jl
ml-jl |
post-ind |
| Prior distributions |
prior-flat
prior-uni
prior-inf
prior-emp
prior-conj
prior-maxent
prior-eb
prior-ref |
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| Bayesian inference |
eb
vb |
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bayes-th
bayes-rule |