hpaDist0: Fast pdf and cdf for standardized univariate PGN distribution

In hpa: Distributions Hermite Polynomial Approximation

Fast pdf and cdf for standardized univariate PGN distribution

Description

These functions use fast algorithms to calculate densities and probabilities (along with their derivatives) related to the standardized PGN distribution.

Usage

dhpa0(
  x,
  pc,
  mean = 0,
  sd = 1,
  is_parallel = FALSE,
  log = FALSE,
  is_validation = TRUE,
  is_grad = FALSE
)

phpa0(
  x,
  pc,
  mean = 0,
  sd = 1,
  is_parallel = FALSE,
  log = FALSE,
  is_validation = TRUE,
  is_grad = FALSE
)

Arguments

x	numeric vector of function arguments.
pc	polynomial coefficients without the first term.
mean	expected value (mean) of the distribution.
sd	standard deviation of the distribution.
is_parallel	logical; if TRUE then multiple cores will be used for some calculations. Currently unavailable.
log	logical; if TRUE then probabilities p are given as log(p) or derivatives will be given with respect to log(p).
is_validation	logical value indicating whether function input arguments should be validated. Set it to FALSE for a slight performance boost (default value is TRUE).
is_grad	logical; if TRUE then function returns gradients with respect to x and pc (default is FALSE).

Details

Functions dhpa0 and phpa0 are similar to dhpa and phpa, respectively. However, there are two key differences. First, dhpa0 and phpa0 deal only with univariate PGN distributions. Second, this distribution is standardized to zero mean and unit variance. Moreover pc is similar to pol_coefficients argument of dhpa but without the first component, i.e., pc = pol_coefficients[-1]. Also mean and sd are not the arguments of the normal density but actual mean and standard deviation of the resulting distribution. So if these arguments are different from 0 and 1 correspondingly then standardized PGN distribution will be linearly transformed to have mean mean and standard deviation sd.

Value

Both functions return a list. Function dhpa0 returns a list with element named "den" that is a numeric vector of density values. Function phpa0 returns a list with element named "prob" that is a numeric vector of probabilities.

If is_grad = TRUE, then elements "grad_x" and "grad_pc" will be added to the list containing gradients with respect to input argument x and parameters pc, respectively. If log = TRUE, then additional elements will be added to the list containing density, probability and gradient values for logarithms of corresponding functions. These elements will be named as "grad_x_log", "grad_pc_log", "prob_log" and "den_log".

Examples

# Calculate density and probability of standardized PGN distribution
  # distribution parameters
pc <- c(0.5, -0.2)
  # function arguments
x <- c(-0.3, 0.8, 1.5)
  # probability density function
dhpa0(x, pc)
  # cumulative distribution function
phpa0(x, pc)

# Additionally calculate gradients with respect to arguments
# and parameters of the PGN distribution
dhpa0(x, pc, is_grad = TRUE)
phpa0(x, pc, is_grad = TRUE)

# Let X be a standardized PGN random variable and repeat
# the calculations for 2 * X + 1
dhpa0(x, pc, is_grad = TRUE, mean = 1, sd = 2)
phpa0(x, pc, is_grad = TRUE, mean = 1, sd = 2)

hpa documentation built on April 14, 2026, 5:09 p.m.