Unif {joker} | R Documentation |
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 signature 'Unif,numeric'
d(distr, x, log = FALSE)
## S4 method for signature 'Unif,numeric'
p(distr, q, lower.tail = TRUE, log.p = FALSE)
## S4 method for signature 'Unif,numeric'
qn(distr, p, lower.tail = TRUE, log.p = FALSE)
## S4 method for signature 'Unif,numeric'
r(distr, n)
## S4 method for signature 'Unif'
mean(x)
## S4 method for signature 'Unif'
median(x)
## S4 method for signature 'Unif'
mode(x)
## S4 method for signature 'Unif'
var(x)
## S4 method for signature 'Unif'
sd(x)
## S4 method for signature 'Unif'
skew(x)
## S4 method for signature 'Unif'
kurt(x)
## S4 method for signature 'Unif'
entro(x)
llunif(x, min, max)
## S4 method for signature 'Unif,numeric'
ll(distr, x)
eunif(x, type = "mle", ...)
## S4 method for signature 'Unif,numeric'
mle(distr, x, na.rm = FALSE)
## S4 method for signature 'Unif,numeric'
me(distr, x, na.rm = FALSE)
Arguments
min , max |
numeric. The distribution parameters. |
distr |
an object of class |
x |
For the density function, |
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 |
numeric. Vector of probabilities. |
n |
number of observations. If |
type |
character, case ignored. The estimator type (mle or me). |
... |
extra arguments. |
na.rm |
logical. Should the |
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 .
Value
Each type of function returns a different type of object:
Distribution Functions: When supplied with one argument (
distr
), thed()
,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
andx
), 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.
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