distributions {joker}R Documentation

Distribution S4 Classes

Description

A collection of S4 classes that provide a flexible and structured way to work with probability distributions.

Usage

d(distr, x, ...)

p(distr, q, ...)

qn(distr, p, ...)

r(distr, n, ...)

Arguments

distr

an object of class Distribution or one of its subclasses.

x

For the density function, x is a numeric vector of quantiles. For the moments functions, x is an object of class Distribution or one of its subclasses. For the log-likelihood and the estimation functions, x is the sample of observations.

...

extra arguments.

q

numeric. Vector of quantiles.

p

numeric. Vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Details

These S4 generic methods can work both as functions and as functionals (functions that return functions). The available distribution families are coded as S4 classes, specifically subclasses of the Distribution superclass. The methods can be used in two ways:

Option 1: If both the distr argument and x or n are supplied, then the function is evaluated directly, as usual.

Option 2: If only the distr argument is supplied, the method returns a function that takes as input the missing argument x or n, allowing the user to work with the function object itself. See examples.

Looking for a specific distribution family? This help page is general. Use the help page of each distribution to see the available methods for the class, details, and examples. Check the See Also section.

Value

Each type of function returns a different type of object:

Functions

See Also

moments, loglikelihood, estimation, Bern, Beta, Binom, Cat, Cauchy, Chisq, Dir, Exp, Fisher, Gam, Geom, Laplace, Lnorm, Multigam, Multinom, Nbinom, Norm, Pois, Stud, Unif, Weib

Examples

# -----------------------------------------------------
# Beta Distribution Example
# -----------------------------------------------------

# Create the distribution
a <- 3
b <- 5
D <- Beta(a, b)

# ------------------
# dpqr Functions
# ------------------

d(D, c(0.3, 0.8, 0.5)) # density function
p(D, c(0.3, 0.8, 0.5)) # distribution function
qn(D, c(0.4, 0.8)) # inverse distribution function
x <- r(D, 100) # random generator function

# alternative way to use the function
df <- d(D) ; df(x) # df is a function itself

# ------------------
# Moments
# ------------------

mean(D) # Expectation
var(D) # Variance
sd(D) # Standard Deviation
skew(D) # Skewness
kurt(D) # Excess Kurtosis
entro(D) # Entropy
finf(D) # Fisher Information Matrix

# List of all available moments
mom <- moments(D)
mom$mean # expectation

# ------------------
# Point Estimation
# ------------------

ll(D, x)
llbeta(x, a, b)

ebeta(x, type = "mle")
ebeta(x, type = "me")
ebeta(x, type = "same")

mle(D, x)
me(D, x)
same(D, x)
e(D, x, type = "mle")

mle("beta", x) # the distr argument can be a character

# ------------------
# Estimator Variance
# ------------------

vbeta(a, b, type = "mle")
vbeta(a, b, type = "me")
vbeta(a, b, type = "same")

avar_mle(D)
avar_me(D)
avar_same(D)

v(D, type = "mle")

[Package joker version 0.14.2 Index]