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#' Create a LogNormal distribution
#'
#' A random variable created by exponentiating a [Normal()]
#' distribution. Taking the log of LogNormal data returns in
#' [Normal()] data.
#'
#' @param log_mu The location parameter, written \eqn{\mu} in textbooks.
#' Can be any real number. Defaults to `0`.
#' @param log_sigma The scale parameter, written \eqn{\sigma} in textbooks.
#' Can be any positive real number. Defaults to `1`.
#'
#' @return A `LogNormal` object.
#' @export
#'
#' @family continuous distributions
#'
#' @details
#'
#' We recommend reading this documentation on
#' <https://alexpghayes.github.io/distributions3/>, where the math
#' will render with additional detail and much greater clarity.
#'
#' In the following, let \eqn{X} be a LogNormal random variable with
#' success probability `p` = \eqn{p}.
#'
#' **Support**: \eqn{R^+}
#'
#' **Mean**: \eqn{\exp(\mu + \sigma^2/2)}
#'
#' **Variance**: \eqn{[\exp(\sigma^2)-1]\exp(2\mu+\sigma^2)}
#'
#' **Probability density function (p.d.f)**:
#'
#' \deqn{
#' f(x) = \frac{1}{x \sigma \sqrt{2 \pi}} \exp \left(-\frac{(\log x - \mu)^2}{2 \sigma^2} \right)
#' }{
#' f(x) = \frac{1}{x \sigma \sqrt{2 \pi}} \exp (-\frac{(\log x - \mu)^2}{2 \sigma^2})
#' }
#'
#' **Cumulative distribution function (c.d.f)**:
#'
#' \deqn{F(x) = \frac{1}{2} + \frac{1}{2\sqrt{pi}}\int_{-x}^x e^{-t^2} dt}
#'
#' **Moment generating function (m.g.f)**:
#' Undefined.
#'
#'
#' @examples
#'
#' set.seed(27)
#'
#' X <- LogNormal(0.3, 2)
#' X
#'
#' random(X, 10)
#'
#' pdf(X, 2)
#' log_pdf(X, 2)
#'
#' cdf(X, 4)
#' quantile(X, 0.7)
LogNormal <- function(log_mu = 0, log_sigma = 1) {
stopifnot(
"parameter lengths do not match (only scalars are allowed to be recycled)" =
length(log_mu) == length(log_sigma) | length(log_mu) == 1 | length(log_sigma) == 1
)
d <- data.frame(log_mu = log_mu, log_sigma = log_sigma)
class(d) <- c("LogNormal", "distribution")
d
}
#' @export
mean.LogNormal <- function(x, ...) {
rlang::check_dots_used()
mu <- x$log_mu
sigma <- x$log_sigma
rval <- exp(mu + sigma^2 / 2)
setNames(rval, names(x))
}
#' @export
variance.LogNormal <- function(x, ...) {
mu <- x$log_mu
sigma <- x$log_sigma
rval <- (exp(sigma^2) - 1) * exp(2 * mu + sigma^2)
setNames(rval, names(x))
}
#' @export
skewness.LogNormal <- function(x, ...) {
mu <- x$log_mu
sigma <- x$log_sigma
rval <- (exp(sigma^2) + 2) * sqrt(exp(sigma^2) - 1)
setNames(rval, names(x))
}
#' @export
kurtosis.LogNormal <- function(x, ...) {
mu <- x$log_mu
sigma <- x$log_sigma
rval <- exp(4 * sigma^2) + 2 * exp(3 * sigma^2) + 3 * exp(2 * sigma^2) - 6
setNames(rval, names(x))
}
#' Draw a random sample from a LogNormal distribution
#'
#' @inherit LogNormal examples
#'
#' @param x A `LogNormal` object created by a call to [LogNormal()].
#' @param n The number of samples to draw. Defaults to `1L`.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param ... Unused. Unevaluated arguments will generate a warning to
#' catch mispellings or other possible errors.
#'
#' @family LogNormal distribution
#'
#' @return In case of a single distribution object or `n = 1`, either a numeric
#' vector of length `n` (if `drop = TRUE`, default) or a `matrix` with `n` columns
#' (if `drop = FALSE`).
#' @export
#'
random.LogNormal <- function(x, n = 1L, drop = TRUE, ...) {
n <- make_positive_integer(n)
if (n == 0L) {
return(numeric(0L))
}
FUN <- function(at, d) rlnorm(n = at, meanlog = d$log_mu, sdlog = d$log_sigma)
apply_dpqr(d = x, FUN = FUN, at = n, type = "random", drop = drop)
}
#' Evaluate the probability mass function of a LogNormal distribution
#'
#' Please see the documentation of [LogNormal()] for some properties
#' of the LogNormal distribution, as well as extensive examples
#' showing to how calculate p-values and confidence intervals.
#'
#' @inherit LogNormal examples
#'
#' @param d A `LogNormal` object created by a call to [LogNormal()].
#' @param x A vector of elements whose probabilities you would like to
#' determine given the distribution `d`.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param elementwise logical. Should each distribution in \code{d} be evaluated
#' at all elements of \code{x} (\code{elementwise = FALSE}, yielding a matrix)?
#' Or, if \code{d} and \code{x} have the same length, should the evaluation be
#' done element by element (\code{elementwise = TRUE}, yielding a vector)? The
#' default of \code{NULL} means that \code{elementwise = TRUE} is used if the
#' lengths match and otherwise \code{elementwise = FALSE} is used.
#' @param ... Arguments to be passed to \code{\link[stats]{dlnorm}}.
#' Unevaluated arguments will generate a warning to catch mispellings or other
#' possible errors.
#'
#' @family LogNormal distribution
#'
#' @return In case of a single distribution object, either a numeric
#' vector of length `probs` (if `drop = TRUE`, default) or a `matrix` with
#' `length(x)` columns (if `drop = FALSE`). In case of a vectorized distribution
#' object, a matrix with `length(x)` columns containing all possible combinations.
#' @export
#'
pdf.LogNormal <- function(d, x, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) dlnorm(x = at, meanlog = d$log_mu, sdlog = d$log_sigma, ...)
apply_dpqr(d = d, FUN = FUN, at = x, type = "density", drop = drop, elementwise = elementwise)
}
#' @rdname pdf.LogNormal
#' @export
log_pdf.LogNormal <- function(d, x, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) dlnorm(x = at, meanlog = d$log_mu, sdlog = d$log_sigma, log = TRUE)
apply_dpqr(d = d, FUN = FUN, at = x, type = "logLik", drop = drop, elementwise = elementwise)
}
#' Evaluate the cumulative distribution function of a LogNormal distribution
#'
#' @inherit LogNormal examples
#'
#' @param d A `LogNormal` object created by a call to [LogNormal()].
#' @param x A vector of elements whose cumulative probabilities you would
#' like to determine given the distribution `d`.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param elementwise logical. Should each distribution in \code{d} be evaluated
#' at all elements of \code{x} (\code{elementwise = FALSE}, yielding a matrix)?
#' Or, if \code{d} and \code{x} have the same length, should the evaluation be
#' done element by element (\code{elementwise = TRUE}, yielding a vector)? The
#' default of \code{NULL} means that \code{elementwise = TRUE} is used if the
#' lengths match and otherwise \code{elementwise = FALSE} is used.
#' @param ... Arguments to be passed to \code{\link[stats]{plnorm}}.
#' Unevaluated arguments will generate a warning to catch mispellings or other
#' possible errors.
#'
#' @family LogNormal distribution
#'
#' @return In case of a single distribution object, either a numeric
#' vector of length `probs` (if `drop = TRUE`, default) or a `matrix` with
#' `length(x)` columns (if `drop = FALSE`). In case of a vectorized distribution
#' object, a matrix with `length(x)` columns containing all possible combinations.
#' @export
#'
cdf.LogNormal <- function(d, x, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) plnorm(q = at, meanlog = d$log_mu, sdlog = d$log_sigma, ...)
apply_dpqr(d = d, FUN = FUN, at = x, type = "probability", drop = drop, elementwise = elementwise)
}
#' Determine quantiles of a LogNormal distribution
#'
#' @inherit LogNormal examples
#' @inheritParams random.LogNormal
#'
#' @param probs A vector of probabilities.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param elementwise logical. Should each distribution in \code{x} be evaluated
#' at all elements of \code{probs} (\code{elementwise = FALSE}, yielding a matrix)?
#' Or, if \code{x} and \code{probs} have the same length, should the evaluation be
#' done element by element (\code{elementwise = TRUE}, yielding a vector)? The
#' default of \code{NULL} means that \code{elementwise = TRUE} is used if the
#' lengths match and otherwise \code{elementwise = FALSE} is used.
#' @param ... Arguments to be passed to \code{\link[stats]{qlnorm}}.
#' Unevaluated arguments will generate a warning to catch mispellings or other
#' possible errors.
#'
#' @return In case of a single distribution object, either a numeric
#' vector of length `probs` (if `drop = TRUE`, default) or a `matrix` with
#' `length(probs)` columns (if `drop = FALSE`). In case of a vectorized
#' distribution object, a matrix with `length(probs)` columns containing all
#' possible combinations.
#' @export
#'
#' @family LogNormal distribution
#'
quantile.LogNormal <- function(x, probs, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) qlnorm(p = at, meanlog = d$log_mu, sdlog = d$log_sigma, ...)
apply_dpqr(d = x, FUN = FUN, at = probs, type = "quantile", drop = drop, elementwise = elementwise)
}
#' Fit a Log Normal distribution to data
#'
#' @param d A `LogNormal` object created by a call to [LogNormal()].
#' @param x A vector of data.
#' @param ... Unused.
#'
#' @family LogNormal distribution
#'
#' @return A `LogNormal` object.
#' @export
#'
fit_mle.LogNormal <- function(d, x, ...) {
ss <- suff_stat(d, x, ...)
LogNormal(ss$mu, ss$sigma)
}
#' Compute the sufficient statistics for a Log-normal distribution from data
#'
#' @inheritParams fit_mle.LogNormal
#'
#' @return A named list of the sufficient statistics of the normal distribution:
#'
#' - `mu`: The sample mean of the log of the data.
#' - `sigma`: The sample standard deviation of the log of the data.
#' - `samples`: The number of samples in the data.
#'
#' @export
#'
suff_stat.LogNormal <- function(d, x, ...) {
valid_x <- x > 0
if (any(!valid_x)) stop("`x` must be a vector of positive real numbers")
log_x <- log(x)
list(mu = mean(log_x), sigma = sd(log_x), samples = length(x))
}
#' Return the support of the LogNormal distribution
#'
#' @param d An `LogNormal` object created by a call to [LogNormal()].
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param ... Currently not used.
#'
#' @return A vector of length 2 with the minimum and maximum value of the support.
#'
#' @export
support.LogNormal <- function(d, drop = TRUE, ...) {
rlang::check_dots_used()
min <- rep(0, length(d))
max <- rep(Inf, length(d))
make_support(min, max, d, drop = drop)
}
#' @exportS3Method
is_discrete.LogNormal <- function(d, ...) {
rlang::check_dots_used()
setNames(rep.int(FALSE, length(d)), names(d))
}
#' @exportS3Method
is_continuous.LogNormal <- function(d, ...) {
rlang::check_dots_used()
setNames(rep.int(TRUE, length(d)), names(d))
}
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