feat: initialize statistical functions

for issue #16

R/stat-logit.R

@@ -0,0 +1,45 @@
+#' logit
+#'
+#' The `logit` function in mathematics is the `quantile` associated with the standard
+#' [logistic distribution](https://en.wikipedia.org/wiki/Logistic_distribution).
+#'
+#' The `logit` is used widely as a method of transforming data for modelling purposes.
+#'
+#' @param p probability, where 0 < *p* < 1.
+#'
+#' @return Log of p/(1-p)
+#' @export
+#'
+#' @examples
+#' logit(.25)
+logit <- function(p) {
+
+  stopifnot(
+    length(p[p < 0]) == 0,
+    length(p[p > 1]) == 0
+  )
+
+  log(p / (1 - p))
+
+}
+
+#' dnorm_logit
+#'
+#' Lognormal Density Function
+#'
+#' @param p probability at which to evaluate the density function
+#' @param mean_logit Mean of logarithmic values
+#' @param sd_logit Standard Deviation of logarithmic values.
+#'
+#' @return z-value representing output of a given value of X
+#' @export
+#'
+#' @examples
+#' dnorm_logit()
+dnorm_logit <- function(p, mean_logit, sd_logit){
+
+  z <- 1 / (sd_logit * sqrt(2 * pi)) * 1 / (p * (1 - p)) * exp(-(logit(p) - mean_logit)^2 / (2 * sd_logit^2))
+
+  return(z)
+
+}