Compute count probabilities using convolution

Description

Compute count probabilities using one of several convolution methods. dCount_conv_bi does the computations for the distributions with builtin support in this package.

dCount_conv_user does the same using a user defined survival function.

Usage

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dCount_conv_bi(x, distPars, dist = c("weibull", "gamma", "gengamma", "burr"),
  method = c("dePril", "direct", "naive"), nsteps = 100, time = 1,
  extrap = TRUE, log = FALSE)

dCount_conv_user(x, distPars, extrapolPars, survR, method = c("dePril",
  "direct", "naive"), nsteps = 100, time = 1, extrap = TRUE,
  log = FALSE)

Arguments

x

integer (vector), the desired count values.

distPars

Rcpp::List with distribution specific slots, see details.

dist

character name of the built-in distribution, see details.

method

character string, the method to use, see Details.

nsteps

unsiged integer, number of steps used to compute the integral.

time

double, time at wich to compute the probabilities. Set to 1 by default.

extrap

logical, if TRUE, Richardson extrapolation will be applied to improve accuracy.

log

logical, if TRUE the log-probability will be returned.

extrapolPars

vector of length 2, the extrapolation values.

survR

function, user supplied survival function; should have signature function(t, distPars), where t is a positive real number (the time where the survival function is evaluated) and distPars is a list of distribution parameters. It should return a double value.

Details

dCount_conv_bi computes count probabilities using one of several convolution methods for the distributions with builtin support in this package.

The following convolution methods are implemented: "dePril", "direct", and "naive".

The builtin distributions currently are Weibull, gamma, generalised gamma and Burr.

Value

vector of probabilities P(x(i),\ i = 1, ..., n) where n is the length of x.

Examples

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x <- 0:10
lambda <- 2.56
p0 <- dpois(x, lambda)
ll <- sum(dpois(x, lambda, TRUE))

err <- 1e-6
## all-probs convolution approach
distPars <- list(scale = lambda, shape = 1)
pmat_bi <- dCount_conv_bi(x, distPars, "weibull", "direct",
                          nsteps = 200)

## user pwei
pwei_user <- function(tt, distP) {
    alpha <- exp(-log(distP[["scale"]]) / distP[["shape"]])
    pweibull(q = tt, scale = alpha, shape = distP[["shape"]],
             lower.tail = FALSE)
}

pmat_user <- dCount_conv_user(x, distPars, c(1, 2), pwei_user, "direct",
                              nsteps = 200)
max((pmat_bi - p0)^2 / p0)
max((pmat_user - p0)^2 / p0)

## naive convolution approach
pmat_bi <- dCount_conv_bi(x, distPars, "weibull", "naive",
                          nsteps = 200)
pmat_user <- dCount_conv_user(x, distPars, c(1, 2), pwei_user, "naive",
                              nsteps = 200)
max((pmat_bi- p0)^2 / p0)
max((pmat_user- p0)^2 / p0)

## dePril conv approach
pmat_bi <- dCount_conv_bi(x, distPars, "weibull", "dePril",
                          nsteps = 200)
pmat_user <- dCount_conv_user(x, distPars, c(1, 2), pwei_user, "dePril",
                              nsteps = 200)
max((pmat_bi- p0)^2 / p0)
max((pmat_user- p0)^2 / p0)

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