version 0.1.0

DESCRIPTION

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+Package: tpwb
+Type: Package
+Title: The Three Parameter Weibull Distribution
+Version: 0.1.0
+Authors@R: c(person("Atchanut","Rattanalertnusorn",role=c("aut","cre"),
+                 email="atchanut_r@rmutt.ac.th"))
+Maintainer: Atchanut Rattanalertnusorn <atchanut_r@rmutt.ac.th>
+Description: Density, distribution function, the quantile function, 
+    random generation function, and maximum likelihood estimation. 
+License: GPL-3
+Language: en-US
+Encoding: UTF-8
+RoxygenNote: 7.1.2
+Imports: graphics, stats
+Suggests: testthat (>= 3.0.0)
+Config/testthat/edition: 3
+NeedsCompilation: no
+Packaged: 2024-05-09 02:36:30 UTC; COM
+Author: Atchanut Rattanalertnusorn [aut, cre]
+Repository: CRAN
+Date/Publication: 2024-05-10 13:50:02 UTC

MD5

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+4b1160372b65448eab18a6fd160d459c *DESCRIPTION
+d4aa8aa7aaa0abb8e5541d3f748e00d3 *NAMESPACE
+38424077dc514030427ba3aa30d1c207 *R/cdfplot.R
+5c667207fc1eac951396a81e6ec1fa8b *R/mlewb.R
+d6e643bcfd8ef123b71606d495be3b4a *R/pdfplot.R
+fdb1009f2f2143edb082d2fd0255ed91 *R/tpwb.R
+6322b3439dfe6f15f81c31dda9bfdf69 *man/cdfplot.Rd
+c294c9280a90169d3ff9b0d3762c01ff *man/mlewb.Rd
+26c239f3c7763fe5b1003cdf299dc3f7 *man/pdfplot.Rd
+447c9ffba14021de220ed34320b4209d *man/tpwb.Rd
+d7505900994f5d5932847f5f6af8aceb *tests/testthat.R
+92e6d751800eee84fb9545e6909441fe *tests/testthat/Rplots.pdf
+6105f483b3fcbe42ef85d768203c2aaa *tests/testthat/test-cdfplot.R
+030f505c913cecda94aeff482e74281b *tests/testthat/test-dtpwb.R
+82f81fc3c40948d3abbe1b72c855c3e1 *tests/testthat/test-mlewb.R
+9d85a879afdc97fa25abe21334a35bf0 *tests/testthat/test-pdfplot.R
+48536e79ecb66ded8120a83f1fb3e386 *tests/testthat/test-ptpwb.R
+3725bfe9f6198572c47f266042e168c1 *tests/testthat/test-qtpwb.R
+ca4b78fd216f9ca079fe99b2403dfac9 *tests/testthat/test-rtpwb.R
+3fa51c69ac31f52437971299f78b72da *tests/testthat/test-tpwb.R

NAMESPACE

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+# Generated by roxygen2: do not edit by hand
+
+export(cdfplot)
+export(dtpwb)
+export(mlewb)
+export(pdfplot)
+export(ptpwb)
+export(qtpwb)
+export(rtpwb)
+import(graphics)
+import(stats)

R/cdfplot.R

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+#' Distribution function plot of the three-parameter Weibull distribution
+#'
+#' Distribution function plot of the three-parameter Weibull distribution with specified \code{shape}, \code{scale} and \code{location}.
+#'
+#' @param x     vector of quantiles
+#' @param shape shape parameter (\eqn{\beta}) of the three-parameter Weibull distribution, where \eqn{\beta >0}.
+#' @param scale scale parameter (\eqn{\alpha}) of the three-parameter Weibull distribution, where \eqn{\alpha > 0}.
+#' @param location location parameter (\eqn{\delta}) of the three-parameter Weibull distribution, where \eqn{\delta \ge 0}.
+#'
+#' @return Distribution function plot of the three-parameter Weibull distribution.
+#' @export
+#'
+#' @references Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
+#'
+#' @examples
+#' x <- rtpwb(100,1.5,2,1)
+#' cdfplot(x,1.5,2,1)
+#'
+cdfplot <-function(x,shape,scale,location){
+  beta <- shape; alpha <- scale; delta <- location
+  x <- x[x>=delta]
+  xs <- sort(x)
+  fx <- ptpwb(xs,shape = beta, scale = alpha, location = delta )
+  plot(x=xs,y=fx,type = "b",xlab="",ylab="")
+  title(main = "CDF of the three-parameter Weibull distribution",
+        xlab="t or x",ylab="F(t) or F(x)")
+  sshape <- beta
+  sscale <- alpha
+  slocation <- delta
+  txtshape <- paste("shape=",sshape)
+  txtscale <- paste("scale=",sscale)
+  txtlocation <- paste("location=",slocation)
+  leg.txt <- c(txtshape,txtscale,txtlocation)
+  legend("bottomright",legend = leg.txt, pch = 1,title = "parameters")
+}

R/mlewb.R

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+#' Maximum likelihood estimation (MLE) for the three-parameter Weibull distribution.
+#'
+#' This function for estimating parameter of the three-parameter Weibull distribution.
+
+#' @param x        vector of quantiles.
+#' @param shape    shape parameter, where \eqn{\beta > 0}.
+#' @param scale    scale parameter, where \eqn{\alpha > 0}.
+#' @param location location parameter, where \eqn{\delta \ge 0}.
+#'
+#' @return the estimated shape, scale and location values of the three-parameter Weibull distribution.
+#' @export
+#'
+#' @note the result of this function may produce a Warning message, but not effect to the estimated parameter.
+#'
+#' @references Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
+#'
+#' @examples
+#' x<- rtpwb(1000,2,3,1) #n=1000 large sample
+#' mlewb(x,2,3,1)
+#' x<- rtpwb(50,2,3,1) #n=50 medium sample
+#' mlewb(x,2,3,1)
+#' x<- rtpwb(10,2,3,1) #n=10 small sample
+#' mlewb(x,2,3,1)
+mlewb <- function(x,shape,scale,location){
+  negll<- function(par){
+    -sum(dtpwb(x,shape=par[1],scale=par[2],location=par[3],log=TRUE))
+  }
+  objmle<- nlminb(start = c(shape,scale,location),negll)
+  mle.shape <- objmle$par[1]
+  mle.scale <- objmle$par[2]
+  mle.location <- objmle$par[3]
+  return(c(mle.shape,mle.scale,mle.location))
+}

R/pdfplot.R

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+#' Probability density function plot of the three-parameter Weibull distribution
+#'
+#' Probability density function plot of the three-parameter Weibull distribution with specified \code{shape}, \code{scale} and \code{location}.
+#'
+#' @param x     vector of quantiles
+#' @param shape shape parameter (\eqn{\beta}) of the three-parameter Weibull distribution, where \eqn{\beta >0}.
+#' @param scale scale parameter (\eqn{\alpha}) of the three-parameter Weibull distribution, where \eqn{\alpha > 0}.
+#' @param location location parameter (\eqn{\delta}) of the three-parameter Weibull distribution, where \eqn{\delta \ge 0}.
+#'
+#' @return Probability density function plot of the three-parameter Weibull distribution.
+#' @export
+#'
+#' @references Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
+#'
+#' @examples
+#' x <- rtpwb(100,1.5,2,1)
+#' pdfplot(x,1.5,2,1)
+#'
+pdfplot <-function(x,shape,scale,location){
+  beta <- shape; alpha <- scale; delta <- location
+  x <- x[x>=delta]
+  xs <- sort(x)
+  fx <- dtpwb(xs,shape = beta, scale = alpha, location = delta )
+  plot(x=xs,y=fx,type = "b",xlab="",ylab="")
+  title(main = "PDF of the three-parameter Weibull distribution",
+        xlab="t or x",ylab="f(t) or f(x)")
+  sshape <- beta
+  sscale <- alpha
+  slocation <- delta
+  txtshape <- paste("shape=",sshape)
+  txtscale <- paste("scale=",sscale)
+  txtlocation <- paste("location=",slocation)
+  leg.txt <- c(txtshape,txtscale,txtlocation)
+  legend("topright",legend = leg.txt, pch = 1,title = "parameters")
+}

R/tpwb.R

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+#' The three-parameter Weibull distribution(tpwb)
+#'
+#' @description Density, distribution function, quantile function, and random generation function
+#' for the three-parameter Weibull distribution with \code{shape}, \code{scale} and \code{location}
+#'
+#' @param x,q vector of quantiles.
+#' @param p   vector of probabilities
+#' @param n   number of observations. If \code{length(n) > 1}, the length is taken to be the number required.
+#' @param shape  shape parameter, where \eqn{\beta > 0}.
+#' @param scale  scale parameter, where \eqn{\alpha > 0}.
+#' @param location location parameter, where \eqn{\delta \ge 0}.
+#' @param log,log.p   logical; (default = \code{FALSE}), if \code{TRUE}, then probabilities are given as \code{log(p)}.
+#' @param lower.tail  logical; if \code{TRUE} (default), probabilities are \eqn{P[X \le x]}, otherwise, \eqn{P[X > x]}.
+#'
+#' @import graphics
+#' @import stats
+#'
+#' @note If location parameter, \eqn{\delta = 0} , it reduced to the two-parameter Weibull distribution.
+#'
+#'@references Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
+#'
+#' @return
+#' \code{dtpwb} gives the density,
+#' \code{ptpwb} gives the distribution function,
+#' \code{qtpwb} gives the quantile function,
+#' and \code{rtpwb} generates random samples.
+#'
+#' @name tpwb
+#' @examples
+#'
+NULL
+
+#' @export
+#' @rdname tpwb
+#' @examples
+#' x <- rtpwb(20,1.5,3,1)
+#' dtpwb(x,1.5,3,1)
+#' dtpwb(x,1.5,3,1,log=TRUE)
+#'
+dtpwb <- function(x, shape, scale, location=1, log = FALSE){
+  beta<- shape; alpha <- scale; delta <- location
+  xs <- x[x>=delta]
+  fx <- (beta/(alpha^beta))*((xs-delta)^(beta-1))*exp(-((xs-delta)/alpha)^beta)
+  if (log==TRUE)
+    return (log(fx))
+  else
+    return(fx)
+}
+
+#' @export
+#' @rdname tpwb
+#' @examples
+#' q <- rtpwb(20,1.5,3,1)
+#' ptpwb(q,1.5,3,1 )
+#' ptpwb(q,1.5,3,1, lower.tail = FALSE)
+#'
+ptpwb <- function(q, shape, scale,location=1, lower.tail = TRUE, log.p = FALSE){
+  beta<- shape; alpha <- scale; delta <- location
+  xs <- q[q>=delta]
+  cdf <- 1-exp(-((xs-delta)/alpha)^beta)
+  if(lower.tail==TRUE)
+    p <- cdf
+  else
+    p <- 1-cdf
+  if (log.p==TRUE)
+    return (log(p))
+  else
+    return(p)
+}
+
+#' @export
+#' @rdname tpwb
+#' @examples
+#' q <- rtpwb(20,1.5,3,1); q
+#' p<- ptpwb(q,1.5,3,1 ); p
+#' qtpwb(p,1.5,3,1)
+#'
+qtpwb <- function(p, shape, scale, location = 1, lower.tail = TRUE, log.p = FALSE){
+  beta<- shape; alpha <- scale; delta <- location
+  if (log.p==TRUE)
+    p <- exp(p)
+  if (lower.tail == FALSE)
+    p <- 1 - p
+  x <- delta + alpha * (-log(1 - p))^(1/beta)
+  return(x)
+}
+
+#' @export
+#' @rdname tpwb
+#' @examples
+#' rtpwb(5, 1.5, 3, 0) # the same as rweibull(5,1.5,3)
+#' rtpwb(25,0.5, 2, 1)
+#'
+rtpwb <- function(n, shape, scale, location = 1){
+  beta<- shape; alpha <- scale; delta <- location
+  u<- runif(n)
+  if (beta <= 0){
+    stop(paste("beta must be larger than 0!", "\n"))
+  }
+  # x based on the inverse transform method : F(x)=u => x=(inv[F(u)])
+  # where u=runif(n,0,1)
+  x <- delta + alpha*(-log(1 - u))^(1/beta)
+  return(x)
+}