Fisher {joker}R Documentation

Fisher Distribution

Description

The Fisher (F) distribution is an absolute continuous probability distribution that arises frequently in the analysis of variance (ANOVA) and in hypothesis testing. It is defined by two degrees of freedom parameters d_1 > 0 and d_2 > 0.

Usage

Fisher(df1 = 1, df2 = 1)

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

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

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

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

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

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

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

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

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

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

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

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

llf(x, df1, df2)

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

Arguments

df1, df2

numeric. The distribution degrees of freedom parameters.

distr

an object of class Fisher.

x

For the density function, x is a numeric vector of quantiles. For the moments functions, x is an object of class Fisher. For the log-likelihood 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.

Details

The probability density function (PDF) of the F-distribution is given by:

f(x; d_1, d_2) = \frac{\sqrt{\left(\frac{d_1 x}{d_1 x + d_2}\right)^{d_1} \left(\frac{d_2}{d_1 x + d_2}\right)^{d_2}}}{x B(d_1/2, d_2/2)}, \quad x > 0 .

Value

Each type of function returns a different type of object:

See Also

Functions from the stats package: df(), pf(), qf(), rf()

Examples

# -----------------------------------------------------
# Fisher Distribution Example
# -----------------------------------------------------

# Create the distribution
df1 <- 14 ; df2 <- 20
D <- Fisher(df1, df2)

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

d(D, c(0.3, 2, 10)) # density function
p(D, c(0.3, 2, 10)) # 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
median(D) # Median
mode(D) # Mode
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)
llf(x, df1, df2)


[Package joker version 0.14.2 Index]