normalizeGaussian_severalstations: Converts several samples `x` random variable extracted by populations represented by the columns of `data` respectively or `sample` to a normally-distributed samples with assinged mean and standard deviation or vice versa in case `inverse` is `TRUE`

Description

Converts several samples x random variable extracted by populations represented by the columns of data respectively or sample to a normally-distributed samples with assinged mean and standard deviation or vice versa in case inverse is TRUE

Usage

normalizeGaussian_severalstations(
  x,
  data = x,
  cpf = NULL,
  mean = 0,
  sd = 1,
  inverse = FALSE,
  step = NULL,
  prec = 10^-4,
  type = 3,
  extremes = TRUE,
  sample = NULL,
  origin_x = NULL,
  origin_data = origin_x
)

Value

a matrix with the normalized variable or its inverse

Arguments

x: value to be converted
data: a sample of data on which a non-parametric probability distribution is estimated
cpf: cumulative probability distribution. If NULL (default) is calculated as ecdf(data)
mean: mean (expected value) of the normalized random variable. Default is 0.
sd: standard deviation of the normalized random variable. Default is 1.
inverse: logical value. If TRUE the function works inversely (the opposite way). Default is FALSE.
step: vector of values in which step discontinuities of the cumulative probability function occur. Default is NULL
prec: amplitude of the neighbourhood of the step discontinuities where cumulative probability function is treated as non-continuous.
type: see quantile
extremes: logical variable. If TRUE (default) the probability or frequency is multiplied by $$\frac{N}{N+1}$$ where $N$ is the length of data
sample: information on how to sample x and data. Default is NULL, this means that the values of each column of x and data belong to the same sample. If x and data are sampled for each month seperately, it is set to monthly.
origin_x: date corresponding to the first row of x
origin_data: date corresponding to the first row of data

Author

Emanuele Cordano, Emanuele Eccel

Examples

Run this code


if (FALSE) {
library(RMAWGEN)

set.seed(1234)
N <- 30
x <- rexp(N)
y <- x+rnorm(N)
df <- data.frame(x=x,y=y)

dfg <- normalizeGaussian_severalstations(df,data=df,extremes=TRUE,inverse=FALSE)

dfi <- normalizeGaussian_severalstations(dfg,data=df,extremes=TRUE,inverse=TRUE)

N <- 365*2
origin <- "1981-01-01"
x <- rexp(N)
y <- x+rnorm(N)
df <- data.frame(x=x,y=y)

dfgm <- normalizeGaussian_severalstations(df,data=df,extremes=TRUE,
inverse=FALSE,origin_x=origin,origin_data=origin,sample="monthly")

dfim <- normalizeGaussian_severalstations(dfg,data=df,extremes=TRUE,
inverse=TRUE,origin_x=origin,origin_data=origin,sample="monthly")


## Compatibility with 'lubridate' package


library(lubridate)


N <- 30
x <- rexp(N)
y <- x+rnorm(N)
df <- data.frame(x=x,y=y)

dfg <- normalizeGaussian_severalstations(df,data=df,extremes=TRUE,inverse=FALSE)

dfi <- normalizeGaussian_severalstations(dfg,data=df,extremes=TRUE,inverse=TRUE)

N <- 365*2
origin <- "1981-01-01"
x <- rexp(N)
y <- x+rnorm(N)
df <- data.frame(x=x,y=y)

dfgm <- normalizeGaussian_severalstations(df,data=df,extremes=TRUE,
inverse=FALSE,origin_x=origin,origin_data=origin,sample="monthly")

dfim <- normalizeGaussian_severalstations(dfg,data=df,extremes=TRUE,
inverse=TRUE,origin_x=origin,origin_data=origin,sample="monthly")
}