The standard symmetric-reflected truncated beta (SSRTB) distribution.

Description

Density, distribution, quantile, random number generation and parameter estimation functions for the SSRTB distribution. Parameter estimation can be based on a weighted or unweighted i.i.d sample and can be carried out numerically.

Usage

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dSSRTB(x, shape1 = 2, shape2 = 3, params = list(shape1, shape2), ...)

pSSRTB(q, shape1 = 2, shape2 = 3, params = list(shape1, shape2), ...)

qSSRTB(p, shape1 = 2, shape2 = 3, params = list(shape1, shape2), ...)

rSSRTB(n, shape1 = 2, shape2 = 3, params = list(shape1, shape2), ...)

eSSRTB(X, w, method = "numerical.MLE", ...)

lSSRTB(X, w, shape1 = 2, shape2 = 3, params = list(shape1, shape2),
  logL = TRUE, ...)

Arguments

x,q

A vector of quantiles.

shape1,shape2

Shape parameters.

params

A list that includes all named parameters.

...

Additional parameters.

p

A vector of probabilities.

n

Number of observations.

X

Sample observations.

w

An optional vector of sample weights.

method

Parameter estimation method.

logL

logical; if TRUE, lSSRTB gives the log-likelihood, otherwise the likelihood is given.

Details

No details as of yet.

Value

dSSRTB gives the density, pSSRTB the distribution function, qSSRTB the quantile function, rSSRTB generates random variables, eSSRTB estimates the parameters and lSSRTB provides the log-likelihood.

Author(s)

Haizhen Wu.

See Also

ExtDist for other standard distributions.

Examples

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# Parameter estimation for a distribution with known shape parameters
X <- rSSRTB(n=500, shape1=2, shape2=10)
est.par <- eSSRTB(X); est.par
plot(est.par)

#  Fitted density curve and histogram
den.x <- seq(min(X),max(X),length=100)
den.y <- dSSRTB(den.x,shape1=est.par$shape1,shape2=est.par$shape2)
hist(X, breaks=10, probability=TRUE, ylim = c(0,1.2*max(den.y)))
lines(den.x, den.y, col="blue")
lines(density(X), lty=2)

# Extracting shape parameters
est.par[attributes(est.par)$par.type=="shape"]

# log-likelihood function
lSSRTB(X,param = est.par)