joker (version 0.14.2)

Unif: Uniform Distribution

Description

The Uniform distribution is an absolute continuous probability distribution where all intervals of the same length within the distribution's support are equally probable. It is defined by two parameters: the lower bound \(a\) and the upper bound \(b\), with \(a < b\).

Usage

Unif(min = 0, max = 1)
# S4 method for Unif,numeric
d(distr, x, log = FALSE)
# S4 method for Unif,numeric
p(distr, q, lower.tail = TRUE, log.p = FALSE)
# S4 method for Unif,numeric
qn(distr, p, lower.tail = TRUE, log.p = FALSE)
# S4 method for Unif,numeric
r(distr, n)
# S4 method for Unif
mean(x)
# S4 method for Unif
median(x)
# S4 method for Unif
mode(x)
# S4 method for Unif
var(x)
# S4 method for Unif
sd(x)
# S4 method for Unif
skew(x)
# S4 method for Unif
kurt(x)
# S4 method for Unif
entro(x)
llunif(x, min, max)
# S4 method for Unif,numeric
ll(distr, x)
eunif(x, type = "mle", ...)
# S4 method for Unif,numeric
mle(distr, x, na.rm = FALSE)
# S4 method for Unif,numeric
me(distr, x, na.rm = FALSE)

Value

Each type of function returns a different type of object:

• Distribution Functions: When supplied with one argument (distr), the d(), p(), q(), r(), ll() functions return the density, cumulative probability, quantile, random sample generator, and log-likelihood functions, respectively. When supplied with both arguments (distr and x), they evaluate the aforementioned functions directly.

• Moments: Returns a numeric, either vector or matrix depending on the moment and the distribution. The moments() function returns a list with all the available methods.

• Estimation: Returns a list, the estimators of the unknown parameters. Note that in distribution families like the binomial, multinomial, and negative binomial, the size is not returned, since it is considered known.

• Variance: Returns a named matrix. The asymptotic covariance matrix of the estimator.

Arguments

min, max

numeric. The distribution parameters.

distr

an object of class Unif.

x

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

log, log.p

logical. Should the logarithm of the probability be returned?

q

numeric. Vector of quantiles.

lower.tail

logical. If TRUE (default), probabilities are \(P(X \leq x)\), otherwise \(P(X > x)\).

p

numeric. Vector of probabilities.

n

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

type

character, case ignored. The estimator type (mle or me).

...

extra arguments.

na.rm

logical. Should the NA values be removed?

Details

The probability density function (PDF) of the Uniform distribution is: $$ f(x; a, b) = \frac{1}{b - a}, \quad a \le x \le b .$$

See Also

Functions from the stats package: dunif(), punif(), qunif(), runif()

Examples

# -----------------------------------------------------
# Uniform Distribution Example
# -----------------------------------------------------

# Create the distribution
a <- 3 ; b <- 5
D <- Unif(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

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

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

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

eunif(x, type = "mle")
eunif(x, type = "me")

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

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