hpaDist0 {hpa}

Fast pdf and cdf for standardized univariate PGN distribution

Description

This function uses fast algorithms to calculate densities and probabilities (along with their derivatives) related to 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 functions 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 respect to log(p).

is_validation

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

is_grad

logical; if TRUE (default) then function returns gradients respect to x and pc.

Details

Functions dhpa0 and phpa0 are similar to dhpa and phpa correspondingly. However there are two key differences. First, dhpa0 and phpa0 are deal with univariate PGN distribution only. Second, this distribution is standardized to zero mean and unit variances. 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 add to the list containing gradients respect to input argument x and parameters pc correspondingly. If log = TRUE then additional elements will be add 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", "grad_prob_log" and "grad_den_log".

Examples

# Calculate density and probability of standartized 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 respect to arguments
# and parameters of the PGN distribution
dhpa0(x, pc, is_grad = TRUE)
phpa0(x, pc, is_grad = TRUE)

# Let's denote by X standardized PGN random variable and repeat
# 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)