version 0.9.2

DESCRIPTION

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+Package: kendallRandomWalks
+Title: Simulate and Visualize Kendall Random Walks and Related
+        Distributions
+Version: 0.9.2
+Authors@R: person("Mateusz", "Staniak", email = "mateusz.staniak@math.uni.wroc.pl", role = c("aut", "cre"))
+Description: Kendall random walks are a continuous-space Markov chains generated
+             by the Kendall generalized convolution. This package provides tools
+             for simulating these random walks and studying distributions
+             related to them. For more information about Kendall random walks see Jasiulis-Gołdyn (2014) <arXiv:1412.0220>.
+Depends: R (>= 3.3)
+License: MIT + file LICENSE
+Encoding: UTF-8
+LazyData: true
+Imports: ggplot2, dplyr, tidyr, EnvStats, tibble, nleqslv
+RoxygenNote: 6.0.1
+Suggests: knitr, rmarkdown, testthat, covr
+VignetteBuilder: knitr
+NeedsCompilation: no
+Packaged: 2018-06-05 18:33:35 UTC; mtst
+Author: Mateusz Staniak [aut, cre]
+Maintainer: Mateusz Staniak <mateusz.staniak@math.uni.wroc.pl>
+Repository: CRAN
+Date/Publication: 2018-06-06 11:17:55 UTC

LICENSE

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+YEAR: 2018
+COPYRIGHT HOLDER: Mateusz Staniak

MD5

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+802161c45338e0f65405afc5c1e31b88 *DESCRIPTION
+127cbfaba59733e6a2c6a1cb068efef0 *LICENSE
+bf40ddb040e1475489436cc818624dbd *NAMESPACE
+d2b472e46a573de5a3285e5a9ddcc53c *NEWS.md
+321cb795d29c29dd544278a672d66d3a *R/barrier_crossing.R
+44742a93c96bea8c1e66ebddf3ee3b11 *R/exact_ladder_moments.R
+0c0ea4b64e63a12cf1c77d1e192a3586 *R/kendallRandomPackage.R
+342bab9561ad2b935f5ef3d3363b1951 *R/simulations_kendall_rw.R
+0cdf1ddbbe6db456b3e2761647dbc7cb *R/stable_kendall_distribution.R
+ecc63136d6a466f61e1ed491dad20450 *R/stable_kendall_fit.R
+b6b60ec945f8a1a226a2bcb0d375a493 *README.md
+b84cc913d6ce0d3aaec243382c8dfe9d *build/vignette.rds
+a48fdecfe2262ed77d8b61e89c783509 *inst/doc/behaviour.R
+7161eac5f4c752b0251bead321523c98 *inst/doc/behaviour.Rmd
+95472fdbb4e06f604fc52498a3335f38 *inst/doc/behaviour.html
+57b6d03ded5319bbee71626929038290 *inst/doc/kendall_rws.R
+a2ba97d109c7e774099396657baf7dee *inst/doc/kendall_rws.Rmd
+11a135a403e922a11064872a6a20344e *inst/doc/kendall_rws.html
+90cfad0d498cc81140a99dcad617506f *man/Qn.Rd
+bac14a58926029a0fea03be2cf7e4b67 *man/U.Rd
+dce1d5e75d456212d0000537beb067d8 *man/Z.Rd
+1bcbad8ce48ea83faf4981ed33c5f6a9 *man/dkend.Rd
+7296860b96d294cfa90a5ddb143e2911 *man/estimate_stable_alpha.Rd
+43a4e3c0349028a7207ff90add1f1ed4 *man/fit_kendall.Rd
+daf8f31ad99cf97685028d8a8e0dec70 *man/fit_separate.Rd
+1e078f529dd4b789c0c4e20b0652a1c8 *man/fit_stable_alpha.Rd
+dc478a9804d04e57d5bcbc1b479ce038 *man/full_loglik_gradient.Rd
+e966dbd9c7ff22c98413cc5fe52e73f0 *man/full_minus_loglik.Rd
+846d3b0a92c23421e9ed338b9f2aa1a3 *man/g_function.Rd
+f0682dab3c6e09294d0cd304504fe201 *man/g_function_single.Rd
+ee19dae30b9c959f00384f52fd5d4fc5 *man/kendallRandomWalks.Rd
+e75c117dd539f486a67685b7f4d8d4d9 *man/kendall_loglik.Rd
+741d52e764454a56e6256747236e1220 *man/ladder_height.Rd
+00a5d7bd2e162f4dfcde322d8c790fdc *man/ladder_moment.Rd
+2a28176cce226256b3ebfb0d38285036 *man/ladder_moment_pmf.Rd
+3387928db5e95dac979483e734955cde *man/mutate_kendall_rw.Rd
+7266e4a1ff17b60c0ba629a1fe93a026 *man/pkend.Rd
+472d9b2fdd3a2ae9e110c8b24924c59f *man/pkendSym.Rd
+654edc804cc98fa738f73cd7c25daf28 *man/plot.kendall_barrier_crossing.Rd
+f561f98fdea9e12c299cbc836b32d2f1 *man/plot.kendall_fit.Rd
+490a4121b7c9eb59a3cf4a46e536288d *man/plot.kendall_simulation.Rd
+a89f67567cf8a3c7e8066700c8fb2e5a *man/print.kendall_barrier_crossing.Rd
+8f0bcbc88a8135114238114a78888895 *man/print.kendall_simulation.Rd
+4f1a7c340be93276c09ad4f942643629 *man/qkend.Rd
+1ce650196a895a90eaf4bf0dfe2ca00b *man/qkendSym.Rd
+ed3c5ae983d3eb2dfc2683d8757ae478 *man/rkend.Rd
+56d91d1a29b9af683a57f03ed9a08fe1 *man/simulateOneTrajectory.Rd
+3154f95637a38863cb5786ae6da69b3d *man/simulate_kendall_rw.Rd
+d8c7c8c7a35a36d36178bae6c9f7aa90 *man/summarise_kendall_rw.Rd
+867c1a92807ac63f896b3832bc347a55 *man/transform_kendall_rw.Rd
+1ccf23728997c0389f54ddc50a4ed5da *tests/testthat.R
+467ab774ad60f93ebb7667bd63db79fc *tests/testthat/test_barriers.R
+a48ae04e756695fa1c0c30d42c222541 *tests/testthat/test_dists.R
+4a31b49bed12cd9b0b7ef16aabab43e6 *tests/testthat/test_fit.R
+991a9cfa7116d3b333f6289e2e971dee *tests/testthat/test_simulations.R
+7161eac5f4c752b0251bead321523c98 *vignettes/behaviour.Rmd
+a2ba97d109c7e774099396657baf7dee *vignettes/kendall_rws.Rmd

NAMESPACE

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+# Generated by roxygen2: do not edit by hand
+
+S3method(plot,kendall_barrier_crossing)
+S3method(plot,kendall_fit)
+S3method(plot,kendall_simulation)
+S3method(print,kendall_barrier_crossing)
+S3method(print,kendall_simulation)
+export(dkend)
+export(estimate_stable_alpha)
+export(fit_kendall)
+export(fit_separate)
+export(fit_stable_alpha)
+export(full_loglik_gradient)
+export(full_minus_loglik)
+export(g_function)
+export(g_function_single)
+export(ladder_height)
+export(ladder_moment)
+export(ladder_moment_pmf)
+export(mutate_kendall_rw)
+export(pkend)
+export(pkendSym)
+export(qkend)
+export(qkendSym)
+export(rkend)
+export(simulate_kendall_rw)
+export(summarise_kendall_rw)
+export(transform_kendall_rw)
+importFrom(dplyr,n)
+importFrom(stats,integrate)
+importFrom(stats,optim)
+importFrom(stats,optimize)
+importFrom(stats,quantile)
+importFrom(stats,rgamma)
+importFrom(stats,sd)

NEWS.md

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+# kendallRandomPackage 0.9.2
+
+* Functions for transformations and summaries of simulations of Kendall random walks
+  (`summarise_kendall_rw` and `mutate_kendall_rw`).
+
+# kendallRandomPackage 0.9.1
+
+* Numerical computation of G function (so also Williamson transform)
+* Exact distribution of first ladder moments
+
+# kendallRandomPackage 0.9.0
+
+* Generic function for printing and plotting simulation objects
+* Barrier crossing simulations and visualizations
+
+# kendallRandomPackage 0.0.0.9000
+
+* Added a `NEWS.md` file to track changes to the package.
+
+
+

R/barrier_crossing.R

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+#' Estimate the distribution of first ladder moment for given level
+#'
+#' NA is returned if the level wasn't crossed. Printing the resulting object
+#' will give summary of the estimated distribution and information whether
+#' level wasn't crossed in some simulations. This information can be used to
+#' pick the right trajectory length for the given level.
+#'
+#' @param simulations kendall_simulation object
+#' @param level Positive numeric
+#'
+#' @return tibble
+#'
+#' @importFrom dplyr n
+#'
+#' @export
+#'
+#' @examples {
+#' kendall_rw <- simulate_kendall_rw(100, 100, runif, 0.5)
+#' estim_ladder <- ladder_moment(kendall_rw, 1000)
+#' estim_ladder
+#' }
+#'
+
+ladder_moment <- function(simulations, level) {
+  if(level < 0) stop("Level must be positive")
+  sim <- id <- sim_id <- NULL
+  kendall_rw <- simulations$simulation
+  kendall_rw <- dplyr::group_by(kendall_rw, sim_id)
+  kendall_rw <- dplyr::mutate(kendall_rw, id = 1:n())
+  all_sims <- dplyr::ungroup(dplyr::distinct(kendall_rw, sim_id))
+  kendall_rw <- dplyr::filter(kendall_rw, sim > level)
+  kendall_rw <- dplyr::summarise(kendall_rw, ladder_moment = min(id))
+  kendall_rw <- dplyr::ungroup(kendall_rw)
+  all_sims <- dplyr::left_join(all_sims, kendall_rw, by = "sim_id")
+
+  class(all_sims) <- c("kendall_barrier_crossing", class(all_sims))
+  all_sims
+}
+
+
+#' Estimate the distribution of first ladder height for given level
+#'
+#' NA is returned if the level wasn't crossed. Printing the resulting object
+#' will give summary of the estimated distribution and information whether
+#' level wasn't crossed in some simulations. This information can be used to
+#' pick the right trajectory length for the given level.
+#'
+#' @param simulations kendall_simulation object
+#' @param level Positive numeric
+#'
+#' @return tibble
+#'
+#' @importFrom dplyr n
+#'
+#' @export
+#'
+#' @examples {
+#'   kendall_rw <- simulate_kendall_rw(100, 100, runif, 0.5)
+#'   estim_ladder <- ladder_height(kendall_rw, 1000)
+#'   estim_ladder
+#' }
+#'
+
+ladder_height <- function(simulations, level) {
+  if(level < 0) stop("Level must be positive")
+  sim <- id <- sim_id <- NULL
+  kendall_rw <- simulations$simulation
+  kendall_rw <- dplyr::group_by(kendall_rw, sim_id)
+  kendall_rw <- dplyr::mutate(kendall_rw, id = 1:n())
+  all_sims <- dplyr::ungroup(dplyr::distinct(kendall_rw, sim_id))
+  kendall_rw <- dplyr::filter(kendall_rw, sim > level)
+  kendall_rw <- dplyr::summarise(kendall_rw, ladder_moment = min(sim))
+  kendall_rw <- dplyr::ungroup(kendall_rw)
+  all_sims <- dplyr::left_join(all_sims, kendall_rw, by = "sim_id")
+
+  class(all_sims) <- c("kendall_barrier_crossing", class(all_sims))
+  all_sims
+}
+
+#' Generic function for printing result of ladder_moment function
+#'
+#' @param x kendall_barrier_crossing object
+#' @param ... Additional arguments
+#'
+#' @return invisible x
+#'
+#' @importFrom stats quantile sd
+#'
+#' @export
+#'
+
+print.kendall_barrier_crossing <- function(x, ...) {
+  quantiles <- quantile(x$ladder_moment, na.rm = T,
+                        probs = seq(0, 1, by = 0.1))
+  labels <- names(quantiles)
+  cat("Mean of the distribution: ", mean(x$ladder_moment, na.rm = T), "\n")
+  cat("Standard deviation of the distribution: ", sd(x$ladder_moment, na.rm = T), "\n")
+  cat("Number of observations: ", max(x$sim_id), "\n")
+  cat("Times the level was not crossed: ", sum(!is.finite(x$ladder_moment)), "\n")
+  cat("Quantiles of the distribution: \n")
+  print(quantiles)
+  invisible(x)
+}
+
+
+#' Generic function for plotting results of ladder_moment function.
+#'
+#' @param x kendall_barrier_crossing object
+#' @param ... Additional arguments
+#'
+#' @return ggplot2
+#'
+#' @export
+#'
+
+plot.kendall_barrier_crossing <- function(x, ...) {
+  mean_value <- mean(x$ladder_moment, na.rm = TRUE)
+  ggplot2::ggplot(x, ggplot2::aes_string(x = 'ladder_moment')) +
+    ggplot2::geom_histogram() +
+    ggplot2::geom_vline(xintercept = mean_value) +
+    ggplot2::theme_bw() +
+    ggplot2::xlab("First ladder moments") +
+    ggplot2::ylab("Count")
+  # dodac tu ecdf
+}

R/exact_ladder_moments.R

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+#' Function G(t) - Williamson transform taken at point 1/t.
+#'
+#' This function return the whole "integrate" object, so precision of the approximation
+#' can be checked.
+#'
+#' @param t Argument to the function.
+#' @param alpha Value of the alpha parameter.
+#' @param density Density function of the step distribution.
+#'
+#' @return Object of class "integrate"
+#'
+#' @importFrom stats integrate
+#'
+#' @examples
+#' g_function_single(5, 0.26, dnorm)
+#'
+#' @export
+#'
+
+g_function_single <- function(t, alpha, density) {
+  force(t)
+  under_integral <- function(x) {
+    (1 - abs(x/t)^(alpha))*density(x)
+  }
+  if(t != 0) {
+    integrate(under_integral, lower = -abs(t), upper = abs(t))
+  } else {
+    fun <- function(x) x
+    integrate(fun, lower = -1, upper = 1)
+  }
+}
+
+
+#' Function G(t) - Williamson transform taken at point 1/t.
+#'
+#' This function return only approximated values. To check their precisions use
+#' g_function_single function with an argument of length 1.
+#'
+#' @param t Argument to the function.
+#' @param alpha Value of the alpha parameter.
+#' @param density Density function of the step distribution.
+#'
+#' @return Object of class "integrate"
+#'
+#' @importFrom stats integrate
+#'
+#' @export
+#'
+#' @examples
+#' g_function(1:5, 0.75, dnorm)
+#'
+#'
+
+g_function <- function(t, alpha, density) {
+  sapply(t, function(x) g_function_single(x, alpha, density)$value)
+}
+
+
+#' Distribution of the first ladder moment.
+#'
+#' @param n Argument to the PDF.
+#' @param level Level a to be crossed.
+#' @param alpha Alpha parameter of Kendall random walk.
+#' @param step_cdf CDF of the step distribution.
+#' @param step_pdf PDF of the step distribution.
+#'
+#' @return Value of PMF of the distribution of first ladder moment
+#'
+#' @export
+#'
+#' @examples
+#' prob <- ladder_moment_pmf(10, 1000, 0.5, pnorm, dnorm)
+#' prob
+#'
+#'
+
+ladder_moment_pmf <- function(n, level, alpha, step_cdf, step_pdf) {
+  Ga <- g_function(level, alpha, step_pdf)
+  Fa <- step_cdf(level)
+  Ha <- 2*Fa - 1 - Ga
+  A <- 1 + Ha/((2*Ga - 1)^2) - Ga/(2*Ga - 1)
+  B <- Ha/((1 - Ga)*(2*Ga - 1))
+  C <- Ga/(2*Ga - 1) - (Ha*Ga)/(((2*Ga - 1)^2)*(1 - Ga))
+
+  A*(2^(-n)) + B*n*((1 - Ga)^2)*(Ga^(n - 1)) + C*(1 - Ga)*(Ga^(n - 1))
+}

R/kendallRandomPackage.R

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+#' kendallRandomWalks: explore and visualize Kendall random walks.
+#'
+#' Kendall random walks are Markov processes generated by the Kendall convolution.
+#' This package helps simulate and visualize these random walks and associated
+#' distributions. It also provides function to fit these distributions to data.
+#'
+#' @section Important functions:
+#' \code{\link{simulate_kendall_rw}} simulates Kendall random walks.
+#'
+#' \code{\link{transform_kendall_rw}} applies scaling and shift to simulated Kendall r.w-s.
+#'
+#' \code{\link{ladder_moment}} estimates the distribution of first ladder moment
+#' by simulating Kendall random walks.
+#'
+#' \code{\link{ladder_height}} estimates the distribution of first ladder height
+#' by simulating Kendall random walks.
+#'
+#' \code{\link{ladder_moment_pmf}} computes the PMF of the distribution of first
+#' ladder moment.
+#'
+#' \code{\link{g_function}} Finds the value of G(t) numerically.
+#'
+#' \code{\link{pkend}}, \code{\link{dkend}}, \code{\link{qkend}}, \code{\link{rkend}}
+#' give CDF, PDF, quantile function and random numbers from stable Kendall distribution.
+#'
+#'
+#' @docType package
+#' @name kendallRandomWalks
+NULL