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## ----knitRPreparations,include=FALSE------------------------------------------
library(knitr)
opts_chunk$set(tidy=FALSE)
## ----Prepa0, include=FALSE, results="hide"------------------------------------
require(distr)
## ----Prepa, echo=FALSE, results="asis"------------------------------
## preparation: set option withSweave to TRUE
require(distr)
distroptions(withSweave = TRUE)
options(width=70)
## ----exam1, eval = TRUE, fig.width=8.0, fig.height=6.5--------------
require(distr)
N <- Norm(mean = 2, sd = 1.3)
P <- Pois(lambda = 1.2)
Z <- 2*N + 3 + P
Z
plot(Z, panel.first = grid(), lwd=3)
p(Z)(0.4)
q(Z)(0.3)
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
Zs <- r(Z)(50)
Zs
## ----DiscrDist, eval = TRUE-----------------------------------------
D <- DiscreteDistribution(supp = c(1,5,7,21), prob = c(0.1,0.1,0.6,0.2))
D
plot(D, panel.first = grid(lwd=2), lwd = 3)
## ----AbscDist, eval = TRUE------------------------------------------
AC <- AbscontDistribution(d = function(x) exp(-abs(x)^3), withStand = TRUE)
AC
plot(AC, panel.first = grid(lwd=2), lwd = 3)
## ----AllClass1, results="asis", echo=TRUE---------------------------
## Class: BinomParameter
setClass("BinomParameter",
representation = representation(size = "numeric", prob = "numeric"),
prototype = prototype(size = 1, prob = 0.5, name =
gettext("Parameter of a Binomial distribution")
),
contains = "Parameter"
)
## ----AllClass2, results="asis", echo=TRUE---------------------------
## Class: binomial distribution
setClass("Binom",
prototype = prototype(
r = function(n){ rbinom(n, size = 1,prob = 0.5) },
d = function(x, log = FALSE){
dbinom(x, size = 1, prob = 0.5, log = log)
},
p = function(q, lower.tail = TRUE, log.p = FALSE ){
pbinom(q, size = 1, prob = 0.5,
lower.tail = lower.tail, log.p = log.p)
},
q = function(p, lower.tail = TRUE, log.p = FALSE ){
qbinom(p, size = 1, prob = 0.5,
lower.tail = lower.tail, log.p = log.p)
},
img = new("Naturals"),
param = new("BinomParameter"),
support = 0:1,
lattice = new("Lattice",
pivot = 0, width = 1, Length = 2, name =
gettext(
"lattice of a Binomial distribution"
)
),
.logExact = TRUE,
.lowerExact = TRUE
),
contains = "LatticeDistribution"
)
## ----BinomDist1, results="asis", echo=TRUE--------------------------
## Access Methods
setMethod("size", "BinomParameter", function(object) object@size)
setMethod("prob", "BinomParameter", function(object) object@prob)
## Replace Methods
setReplaceMethod("size", "BinomParameter",
function(object, value){ object@size <- value; object})
setReplaceMethod("prob", "BinomParameter",
function(object, value){ object@prob <- value; object})
## ----AllGenerics, results="asis", echo=TRUE-------------------------
if(!isGeneric("size"))
setGeneric("size", function(object) standardGeneric("size"))
if(!isGeneric("prob"))
setGeneric("prob", function(object) standardGeneric("prob"))
## ----BinomDist2, results="asis", echo=TRUE--------------------------
setValidity("BinomParameter", function(object){
if(length(prob(object)) != 1)
stop("prob has to be a numeric of length 1")
if(prob(object) < 0)
stop("prob has to be in [0,1]")
if(prob(object) > 1)
stop("prob has to be in [0,1]")
if(length(size(object)) != 1)
stop("size has to be a numeric of length 1")
if(size(object) < 1)
stop("size has to be a natural greater than 0")
if(!identical(floor(size(object)), size(object)))
stop("size has to be a natural greater than 0")
else return(TRUE)
})
## ----BinomDist3, results="asis", echo=TRUE--------------------------
Binom <- function(size = 1,prob = 0.5) new("Binom", size = size, prob = prob)
## ----BinomDist4, results="asis", echo=TRUE--------------------------
## Convolution for two binomial distributions Bin(n1,p1) and Bin(n2,p2)
## Distinguish cases
## p1 == p2 und p1 != p2
setMethod("+", c("Binom","Binom"),
function(e1,e2){
newsize <- size(e1) + size(e2)
if(isTRUE(all.equal(prob(e1),prob(e2))))
return(new("Binom", prob = prob(e1), size = newsize,
.withArith = TRUE))
return(as(e1, "LatticeDistribution") + e2)
})
## ----Prepa2, echo=FALSE, results="asis"-----------------------------
## preparation: set option withSweave to TRUE
require(distrEx)
## ----Expect, results="asis", echo=TRUE------------------------------
setMethod("E", signature(object = "Binom",
fun = "missing",
cond = "missing"),
function(object, low = NULL, upp = NULL, ...){
if(!is.null(low)) if(low <= min(support(object))) low <- NULL
if(!is.null(upp)) if(upp >= max(support(object))) upp <- NULL
if(is.null(low) && is.null(upp))
return(size(object)*prob(object))
else{
if(is.null(low)) low <- -Inf
if(is.null(upp)) upp <- Inf
if(low == -Inf){
if(upp == Inf) return(size(object)*prob(object))
else return(m1df(object, upper = upp, ...))
}else{
E1 <- m1df(object, upper = low, ...)
E2 <- if(upp == Inf)
size(object)*prob(object) else m1df(object, upper = upp, ...)
return(E2-E1)
}
}
})
## ----var, results="asis", echo=TRUE---------------------------------
setMethod("var", signature(x = "Binom"),
function(x,...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
fun <- NULL; cond <- NULL; low <- NULL; upp <- NULL
if(hasArg(low)) low <- dots$low
if(hasArg(upp)) upp <- dots$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(var(as(x,"DiscreteDistribution"),...))
else
return(size(x)*prob(x)*(1-prob(x)))
})
## ----skew, results="asis", echo=TRUE--------------------------------
setMethod("skewness", signature(x = "Binom"),
function(x, ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
fun <- NULL; cond <- NULL; low <- NULL; upp <- NULL
if(hasArg(low)) low <- dots$low
if(hasArg(upp)) upp <- dots$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(skewness(as(x,"DiscreteDistribution"),...))
else
return((1-2*prob(x))/sqrt(size(x)*prob(x)*(1-prob(x))))
})
## ----kurt, results="asis", echo=TRUE--------------------------------
setMethod("kurtosis", signature(x = "Binom"),
function(x, ...){
dots <- match.call(call = sys.call(sys.parent(1)),
expand.dots = FALSE)$"..."
fun <- NULL; cond <- NULL; low <- NULL; upp <- NULL
if(hasArg(low)) low <- dots$low
if(hasArg(upp)) upp <- dots$upp
if(hasArg(fun)||hasArg(cond)||!is.null(low)||!is.null(upp))
return(kurtosis(as(x,"DiscreteDistribution"),...))
else
p <- prob(x)
return((1-6*p*(1-p))/(size(x)*p*(1-p)))
})
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