Chisq {joker}R Documentation

Chi-Square Distribution

Description

The Chi-Square distribution is a continuous probability distribution commonly used in statistical inference, particularly in hypothesis testing and confidence interval estimation. It is defined by the degrees of freedom parameter k > 0.

Usage

Chisq(df = 1)

## S4 method for signature 'Chisq,numeric'
d(distr, x, log = FALSE)

## S4 method for signature 'Chisq,numeric'
p(distr, q, lower.tail = TRUE, log.p = FALSE)

## S4 method for signature 'Chisq,numeric'
qn(distr, p, lower.tail = TRUE, log.p = FALSE)

## S4 method for signature 'Chisq,numeric'
r(distr, n)

## S4 method for signature 'Chisq'
mean(x)

## S4 method for signature 'Chisq'
median(x)

## S4 method for signature 'Chisq'
mode(x)

## S4 method for signature 'Chisq'
var(x)

## S4 method for signature 'Chisq'
sd(x)

## S4 method for signature 'Chisq'
skew(x)

## S4 method for signature 'Chisq'
kurt(x)

## S4 method for signature 'Chisq'
entro(x)

## S4 method for signature 'Chisq'
finf(x)

llchisq(x, df)

## S4 method for signature 'Chisq,numeric'
ll(distr, x)

echisq(x, type = "mle", ...)

## S4 method for signature 'Chisq,numeric'
mle(distr, x, na.rm = FALSE)

## S4 method for signature 'Chisq,numeric'
me(distr, x, na.rm = FALSE)

vchisq(df, type = "mle")

## S4 method for signature 'Chisq'
avar_mle(distr)

## S4 method for signature 'Chisq'
avar_me(distr)

Arguments

df

numeric. The distribution degrees of freedom parameter.

distr

an object of class Chisq.

x

For the density function, x is a numeric vector of quantiles. For the moments functions, x is an object of class Chisq. 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 Chi-Square distribution is given by:

f(x; k) = \frac{1}{2^{k/2}\Gamma(k/2)} x^{k/2 - 1} e^{-x/2}, \quad x > 0.

Value

Each type of function returns a different type of object:

See Also

Functions from the stats package: dchisq(), pchisq(), qchisq(), rchisq()

Examples

# -----------------------------------------------------
# Chi-Square Distribution Example
# -----------------------------------------------------

# Create the distribution
df <- 4
D <- Chisq(df)

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

d(D, c(0.3, 2, 20)) # density function
p(D, c(0.3, 2, 20)) # 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
den <- d(D) ; den(x) # den 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)
llchisq(x, df)

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

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

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

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

vchisq(df, type = "mle")
vchisq(df, type = "me")

avar_mle(D)
avar_me(D)

v(D, type = "mle")

[Package joker version 0.14.2 Index]