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 |
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 |
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:
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: 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)