hpa (version 1.0.1)

truncatedNormalMoment: Calculate k-th order moment of truncated normal distribution

Description

This function iteratively calculates k-th order moment of truncated normal distribution.

Usage

truncatedNormalMoment(k = 1L, x_lower = numeric(0),
  x_upper = numeric(0), mean = 0, sd = 1, pdf_lower = numeric(0),
  cdf_lower = numeric(0), pdf_upper = numeric(0),
  cdf_upper = numeric(0), cdf_difference = numeric(0),
  return_all_moments = FALSE, is_validation = TRUE)

Arguments

k

non-negative integer moment order.

x_lower

numeric vector of lower trancation points.

x_upper

numeric vector of upper trancation points.

mean

numeric expected value.

sd

positive numeric standard deviation.

pdf_lower

non-negative numeric matrix of precalculated normal density functions with mean mean and standard deviation sd at points given by x_lower.

cdf_lower

non-negative numeric matrix of precalculated normal cumulative distribution functions with mean mean and standard deviation sd at points given by x_lower.

pdf_upper

non-negative numeric matrix of precalculated normal density functions with mean mean and standard deviation sd at points given by x_upper.

cdf_upper

non-negative numeric matrix of precalculated normal cumulative distribution functions with mean mean and standard deviation sd at points given by x_upper.

cdf_difference

non-negative numeric matrix of predcalculated cdf_upper-cdf_lower values.

return_all_moments

logical; if TRUE, function returns the matrix of moments of normaly distributed random variable with mean = mean and standard deviation = sd under lower and upper truncation points x_lower and x_upper correspondingly. Note that element in i-th row and j-th column of this matrix corresponds to the i-th observation (j-1)-th order moment.

is_validation

bool value indicating whether function input arguments should be validated. Set it to FALSE for slight perfomance boost (default value is TRUE).

Value

This function returns vector of k-th order moments for normaly distributed random variable with mean = mean and standard deviation = sd under x_lower and x_upper truncation points x_lower and x_upper correspondingly. If return_all_moments is TRUE then see this argument description above for output details.

Details

This function estimates k-th order moment of normal distribution which mean equals to mean and standard deviation equals to sd truncated at points given by x_lower and x_upper. Note that the function is vectorized so you can provide x_lower and x_upper as vectors of equal size. If vectors values for x_lower and x_upper are not provided then their default values will be set to (-9999999999999.1) and (9999999999999.1) correspondingly.

Note that parameter k value automatically converts to integer. So passing non-integer k value will not cause any errors but the calculations will be performed for rounded k value only.

If you have precaulculated density or cumulative distribution functions at standartized truncation points (substract mean and then divide by sd) then provide them throught pdf_lower, pdf_upper, cdf_lower and cdf_upper arguments in order to decrease number of calculations.

Examples

# NOT RUN {
##Calculate 5-th order moment of three truncated normal random variables (x1,x2,x3) 
##which mean is 5 and standard deviation is 3. 
##These random variables truncation points are given as follows:-1<x1<1, 0<x2<2, 1<x3<3.
k <- 3
x_lower <- c(-1, 0, 1)
x_upper <- c(1, 2 ,3)
mean <- 3
sd <- 5

#get the moments
truncatedNormalMoment(k, x_lower, x_upper, mean, sd)

#get matrix of (0-5)-th moments (columns) for each variable (rows)
truncatedNormalMoment(k, x_lower, x_upper, mean, sd, return_all_moments = TRUE)

# }