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stats/dist

src/stats/dist.tur
defn

dist-normal

(dist-normal [mu :float sigma :float] :int)

construct a Normal(mu, sigma) distribution object.

Parameters
mu:float mean
sigma:float standard deviation (> 0)
Returns

:int dist handle. Free with dist-free.

Example
(let [d (dist-normal 0.0 1.0)] (pdf d 0.0))  ; => ~0.3989

Since: ST3

defn

dist-t

(dist-t [df :float] :int)

construct a Student t(df) distribution.

Parameters
df:float degrees of freedom (> 0)
Returns

:int dist handle.

Since: ST3

defn

dist-chi2

(dist-chi2 [df :float] :int)

construct a chi-squared(df) distribution.

Parameters
df:float degrees of freedom (> 0)
Returns

:int dist handle.

Since: ST3

defn

dist-f

(dist-f [df1 :float df2 :float] :int)

construct an F(df1, df2) distribution.

Parameters
df1:float numerator df
df2:float denominator df
Returns

:int dist handle.

Since: ST3

defn

dist-uniform

(dist-uniform [a :float b :float] :int)

construct a Uniform(a, b) distribution.

Parameters
a:float lower bound
b:float upper bound (b > a)
Returns

:int dist handle.

Since: ST4

defn

dist-binomial

(dist-binomial [n :int p :float] :int)

construct a Binomial(n, p) distribution.

Parameters
n:int number of trials
p:float success probability in [0,1]
Returns

:int dist handle.

Since: ST4

defn

dist-poisson

(dist-poisson [lambda :float] :int)

construct a Poisson(lambda) distribution.

Parameters
lambda:float rate parameter (> 0)
Returns

:int dist handle.

Since: ST4

defn

dist-exponential

(dist-exponential [rate :float] :int)

construct an Exponential(rate) distribution.

Parameters
rate:float rate = 1/mean (> 0)
Returns

:int dist handle.

Since: ST4

defn

dist-beta

(dist-beta [alpha :float beta :float] :int)

construct a Beta(alpha, beta) distribution.

Parameters
alpha:float shape1 (> 0)
beta:float shape2 (> 0)
Returns

:int dist handle.

Since: ST4

defn

dist-gamma

(dist-gamma [shape :float rate :float] :int)

construct a Gamma(shape, rate) distribution.

Parameters
shape:float shape parameter (> 0)
rate:float rate = 1/scale (> 0)
Returns

:int dist handle.

Since: ST4

defn

dist-free

(dist-free [d :int] :void)

free a distribution object.

Since: ST3

defn

pdf

(pdf [d :int x :float] :float)

probability density (or mass) at x.

Parameters
d:int dist handle
x:float argument
Returns

:float density / PMF value.

Since: ST3

defn

cdf

(cdf [d :int x :float] :float)

cumulative distribution function P(X <= x).

Parameters
d:int dist handle
x:float argument
Returns

:float P(X <= x) in [0, 1].

Since: ST3

defn

quantile

(quantile [d :int p :float] :float)

inverse CDF (quantile function).

Parameters
d:int dist handle
p:float probability in [0, 1]
Returns

:float x such that CDF(x) ~= p.

Since: ST3

defn

random

(random [d :int rng :int] :float)

draw one sample from a distribution.

Parameters
d:int dist handle
rng:int rng handle (from rng-make)
Returns

:float one sample.

Since: ST3

defn

random-n

(random-n [d :int rng :int n :int] :int)

draw n samples from a distribution into a float64 column.

Parameters
d:int dist handle
rng:int rng handle
n:int number of samples
Returns

:int new float64 column of length n. Caller frees.

Since: ST3

defn

dnorm

(dnorm [x :float mu :float sigma :float] :float)

normal density at x.

Since: ST4

defn

pnorm

(pnorm [x :float mu :float sigma :float] :float)

normal CDF at x.

Since: ST4

defn

qnorm

(qnorm [p :float mu :float sigma :float] :float)

normal quantile at p.

Since: ST4

defn

rnorm

(rnorm [rng :int n :int mu :float sigma :float] :int)

n normal samples.

Since: ST4

defn

dt

(dt [x :float df :float] :float)

t density.

Since: ST4

defn

pt

(pt [x :float df :float] :float)

t CDF.

Since: ST4

defn

qt

(qt [p :float df :float] :float)

t quantile.

Since: ST4

defn

rt

(rt [rng :int n :int df :float] :int)

n t samples.

Since: ST4

defn

dchi2

(dchi2 [x :float df :float] :float)

chi-squared density.

Since: ST4

defn

pchi2

(pchi2 [x :float df :float] :float)

chi-squared CDF.

Since: ST4

defn

qchi2

(qchi2 [p :float df :float] :float)

chi-squared quantile.

Since: ST4

defn

rchi2

(rchi2 [rng :int n :int df :float] :int)

n chi-squared samples.

Since: ST4

defn

df-dist

(df-dist [x :float df1 :float df2 :float] :float)

F density.

Since: ST4

defn

pf-dist

(pf-dist [x :float df1 :float df2 :float] :float)

F CDF.

Since: ST4

defn

qf-dist

(qf-dist [p :float df1 :float df2 :float] :float)

F quantile.

Since: ST4

defn

rf-dist

(rf-dist [rng :int n :int df1 :float df2 :float] :int)

n F samples.

Since: ST4

defn

dunif

(dunif [x :float a :float b :float] :float)

uniform density.

Since: ST4

defn

punif

(punif [x :float a :float b :float] :float)

uniform CDF.

Since: ST4

defn

qunif

(qunif [p :float a :float b :float] :float)

uniform quantile.

Since: ST4

defn

runif

(runif [rng :int n :int a :float b :float] :int)

n uniform samples.

Since: ST4

defn

dbinom

(dbinom [x :float n :int p :float] :float)

binomial PMF.

Since: ST4

defn

pbinom

(pbinom [x :float n :int p :float] :float)

binomial CDF.

Since: ST4

defn

qbinom

(qbinom [p :float n :int pp :float] :float)

binomial quantile.

Since: ST4

defn

rbinom

(rbinom [rng :int n-samp :int n-trials :int p :float] :int)

n binomial samples.

Since: ST4

defn

dpois

(dpois [x :float lambda :float] :float)

Poisson PMF.

Since: ST4

defn

ppois

(ppois [x :float lambda :float] :float)

Poisson CDF.

Since: ST4

defn

qpois

(qpois [p :float lambda :float] :float)

Poisson quantile.

Since: ST4

defn

rpois

(rpois [rng :int n :int lambda :float] :int)

n Poisson samples.

Since: ST4

defn

dexp

(dexp [x :float rate :float] :float)

exponential density.

Since: ST4

defn

pexp

(pexp [x :float rate :float] :float)

exponential CDF.

Since: ST4

defn

qexp

(qexp [p :float rate :float] :float)

exponential quantile.

Since: ST4

defn

rexp

(rexp [rng :int n :int rate :float] :int)

n exponential samples.

Since: ST4

defn

dbeta

(dbeta [x :float alpha :float beta :float] :float)

beta density.

Since: ST4

defn

pbeta

(pbeta [x :float alpha :float beta :float] :float)

beta CDF.

Since: ST4

defn

qbeta

(qbeta [p :float alpha :float beta :float] :float)

beta quantile.

Since: ST4

defn

rbeta

(rbeta [rng :int n :int alpha :float beta :float] :int)

n beta samples.

Since: ST4

defn

dgamma

(dgamma [x :float shape :float rate :float] :float)

gamma density.

Since: ST4

defn

pgamma

(pgamma [x :float shape :float rate :float] :float)

gamma CDF.

Since: ST4

defn

qgamma

(qgamma [p :float shape :float rate :float] :float)

gamma quantile.

Since: ST4

defn

rgamma

(rgamma [rng :int n :int shape :float rate :float] :int)

n gamma samples.

Since: ST4