hsaDist: Probabilities and Moments Hermite Spline Approximation

Description

The set of functions similar to dhpa-like functions. The difference is that instead of polynomial these functions utilize spline.

Usage

dhsa(x, m, knots, mean = 0, sd = 1, log = FALSE)
ehsa(m, knots, mean = 0, sd = 1, power = 1)

Value

Function dhsa returns vector of probabilities of the same length as x. Function ehsa

returns moment value.

Arguments

x: numeric vector of values for which the function should be estimated.
m: numeric matrix which rows correspond to spline intervals while columns represent variables powers. Therefore the element in i-th row and j-th column represents the coefficient associated with the variable that 1) belongs to the i-th interval i.e. between i-th and (i + 1)-th knots 2) raised to the power of (j - 1).
knots: sorted in ascending order numeric vector representing knots of the spline.
mean: expected value of a normal distribution.
sd: standard deviation of a normal distribution.
log: logical; if TRUE then probabilities p are given as log(p) or derivatives will be given respect to log(p).
power: non-negative integer representing the power of the expected value i.e. E(X ^ power) will be estimated.

Details

In contrast to dhpa-like functions these functions may deal with univariate distributions only. In future this functions will be generalized to work with multivariate distributions. The main idea of these functions is to use squared spline instead of squared polynomial in order to provide greater numeric stability and approximation accuracy. To provide spline parameters please use m and knots arguments (i.e. instead of pol_degrees and pol_coefficients arguments that where used to specify the polynomial for dhpa-like functions).

Examples

Run this code

## Examples demonstrating dhsa and ehsa functions application.

# Generate a b-splines
b <- bsplineGenerate(knots = c(-2.1, 1.5, 1.5, 2.2, 3.7, 4.2, 5),
                     degree = 3)
                      
# Combine b-splines into a spline
spline <- bsplineComb(splines = b, weights = c(1.6, -1.2, 3.2))

# Assign parameters using the spline created above
knots <- spline$knots
m <- spline$m
mean <- 1
sd <- 2

# Estimate the density at particular points
x <- c(2, 3.7, 8)
dhsa(x, 
     m = m, knots = knots,
     mean = mean, sd = sd)
     
# Calculate expected value
ehsa(m = m, knots = knots,
     mean = mean, sd = sd,
     power = 1) 
     
# Evaluate the third moment
ehsa(m = m, knots = knots,
     mean = mean, sd = sd,
     power = 3)