moments: Moments - Parametric Quantities of Interest

In joker: Probability Distributions and Parameter Estimation

Moments - Parametric Quantities of Interest

Description

A set of functions that calculate the theoretical moments (expectation, variance, skewness, excess kurtosis) and other important parametric functions (median, mode, entropy, Fisher information) of a distribution.

Usage

moments(x)

mean(x, ...)

median(x, na.rm = FALSE, ...)

mode(x)

var(x, y = NULL, na.rm = FALSE, use)

sd(x, na.rm = FALSE)

skew(x, ...)

kurt(x, ...)

entro(x, ...)

finf(x, ...)

Arguments

x	a Distribution object.
...	extra arguments.
y, use, na.rm	arguments in mean and var standard methods from the stats package not used here.

Details

Given a distribution, these functions calculate the theoretical moments and other parametric quantities of interest. Some distribution-function combinations are not available; for example, the sd() function is available only for univariate distributions.

The moments() function automatically finds the available methods for a given distribution and results all of the results in a list.

Technical Note: The argument of the moment functions does not follow the naming convention of the package, i.e. the Distribution object is names x rather than distr. This is due to the fact that most of the generics are already defined in the stats package (mean, median, mode, var, sd), therefore the first argument was already named x and could not change.

Value

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

Functions

• median(): Median

• mode(): Mode

• var(): Variance

• sd(): Standard Deviation

• skew(): Skewness

• kurt(): Kurtosis

• entro(): Entropy

• finf(): Fisher Information (numeric or matrix)

See Also

distributions, loglikelihood, estimation

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")

joker documentation built on June 8, 2025, 12:12 p.m.