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

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

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

# 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)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> library(ExtDist)

Attaching package: 'ExtDist'

The following object is masked from 'package:stats':

    BIC

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/ExtDist/SSRTB.Rd_%03d_medium.png", width=480, height=480)
> ### Name: SSRTB
> ### Title: The standard symmetric-reflected truncated beta (SSRTB)
> ###   distribution.
> ### Aliases: SSRTB dSSRTB eSSRTB lSSRTB pSSRTB qSSRTB rSSRTB
> 
> ### ** Examples
> 
> # Parameter estimation for a distribution with known shape parameters
> X <- rSSRTB(n=500, shape1=2, shape2=10)
> est.par <- eSSRTB(X); est.par

Parameters for the SSRTB distribution. 
(found using the  numerical.MLE method.)

 Parameter  Type Estimate      S.E.
    shape1 shape 1.963766 0.2577075
    shape2 shape 2.110834 2.8581397


> 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"]
$shape1
[1] 1.963766

$shape2
[1] 2.110834

> 
> # log-likelihood function
> lSSRTB(X,param = est.par)
[1] 58.63162
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>