# R/LogNormal.R In distributions3: Probability Distributions as S3 Objects

#### Documented in cdf.LogNormalfit_mle.LogNormalLogNormallog_pdf.LogNormalpdf.LogNormalquantile.LogNormalrandom.LogNormalsuff_stat.LogNormalsupport.LogNormal

#' 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) {
d <- list(log_mu = log_mu, log_sigma = log_sigma)
class(d) <- c("LogNormal", "distribution")
d
}

#' @export
print.LogNormal <- function(x, ...) {
cat(glue("Lognormal distribution (log_mu = {x$log_mu}, log_sigma = {x$log_sigma})"), "\n")
}

#' @export
mean.LogNormal <- function(x, ...) {
ellipsis::check_dots_used()
mu <- x$log_mu sigma <- x$log_sigma
exp(mu + sigma^2 / 2)
}

#' @export
variance.LogNormal <- function(x, ...) {
mu <- x$log_mu sigma <- x$log_sigma
(exp(sigma^2) - 1) * exp(2 * mu + sigma^2)
}

#' @export
skewness.LogNormal <- function(x, ...) {
mu <- x$log_mu sigma <- x$log_sigma
(exp(sigma^2) + 2) * sqrt(exp(sigma^2) - 1)
}

#' @export
kurtosis.LogNormal <- function(x, ...) {
mu <- x$log_mu sigma <- x$log_sigma
exp(4 * sigma^2) + 2 * exp(3 * sigma^2) + 3 * exp(2 * sigma^2) - 6
}

#' 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 ... Unused. Unevaluated arguments will generate a warning to
#'   catch mispellings or other possible errors.
#'
#' @family LogNormal distribution
#'
#' @return An integer vector of length n.
#' @export
#'
random.LogNormal <- function(x, n = 1L, ...) {
rlnorm(n = n, meanlog = x$log_mu, sdlog = x$log_sigma)
}

#' 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 ... Unused. Unevaluated arguments will generate a warning to
#'   catch mispellings or other possible errors.
#'
#' @family LogNormal distribution
#'
#' @return A vector of probabilities, one for each element of x.
#' @export
#'
pdf.LogNormal <- function(d, x, ...) {
dlnorm(x = x, meanlog = d$log_mu, sdlog = d$log_sigma)
}

#' @rdname pdf.LogNormal
#' @export
log_pdf.LogNormal <- function(d, x, ...) {
dlnorm(x = x, meanlog = d$log_mu, sdlog = d$log_sigma, log = TRUE)
}

#' 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 ... Unused. Unevaluated arguments will generate a warning to
#'   catch mispellings or other possible errors.
#'
#' @family LogNormal distribution
#'
#' @return A vector of probabilities, one for each element of x.
#' @export
#'
cdf.LogNormal <- function(d, x, ...) {
plnorm(q = x, meanlog = d$log_mu, sdlog = d$log_sigma)
}

#' Determine quantiles of a LogNormal distribution
#'
#' @inherit LogNormal examples
#' @inheritParams random.LogNormal
#'
#' @param probs A vector of probabilities.
#' @param ... Unused. Unevaluated arguments will generate a warning to
#'   catch mispellings or other possible errors.
#'
#' @return A vector of quantiles, one for each element of probs.
#' @export
#'
#' @family LogNormal distribution
#'
quantile.LogNormal <- function(x, probs, ...) {
ellipsis::check_dots_used()
qlnorm(p = probs, meanlog = x$log_mu, sdlog = x$log_sigma)
}

#' 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()].
#'
#' @return A vector of length 2 with the minimum and maximum value of the support.
#'
#' @export
support.LogNormal <- function(d){
if(!is_distribution(d)){
message("d has to be a disitrubtion")
stop()
}
return(c(0, Inf))
}


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distributions3 documentation built on Jan. 4, 2022, 1:07 a.m.