combdist {distributionsrd}

Combined distributions

Description

Density, distribution function, quantile function, raw moments and random generation for combined (empirical, single, composite and finite mixture) truncated or complete distributions.

Usage

dcombdist(
  x,
  dist,
  prior = c(1),
  coeff,
  log = FALSE,
  compress = TRUE,
  lowertrunc = 0,
  uppertrunc = Inf
)

pcombdist(
  q,
  dist,
  prior = 1,
  coeff,
  log.p = FALSE,
  lower.tail = TRUE,
  compress = TRUE,
  lowertrunc = NULL,
  uppertrunc = NULL
)

qcombdist(p, dist, prior, coeff, log.p = FALSE, lower.tail = TRUE)

mcombdist(
  r,
  truncation = NULL,
  dist,
  prior = 1,
  coeff,
  lower.tail = TRUE,
  compress = TRUE,
  uppertrunc = 0,
  lowertrunc = Inf
)

rcombdist(n, dist, prior, coeff, uppertrunc = NULL, lowertrunc = NULL)

Arguments

x, q

vector of quantiles

dist

character vector denoting the distribution(s).

prior

Numeric vector of prior coefficients, defaults to single vector with value one.

coeff

list of parameters for the distribution(s).

log, log.p

logical; if TRUE, probabilities p are given as log(p).

compress

Logical indicating whether return values from individual densities of finite mixtures should be gathered or not, defaults to TRUE.

lowertrunc, uppertrunc

lowertrunc- and uppertrunc truncation points, defaults to 0 and Inf respectively

lower.tail

logical; if TRUE (default), probabilities (moments) are P[X \leq x] (E[x^r|X \leq y]), otherwise, P[X > x] (E[x^r|X > y])

p

vector of probabilities

r

rth raw moment of the Pareto distribution

truncation

lower truncation parameter

n

number of observations

Value

dcombdist gives the density, pcombdist gives the distribution function, qcombdist gives the quantile function, mcombdist gives the rth moment of the distribution and rcombdist generates random deviates.

The length of the result is determined by n for rcombdist, and is the maximum of the lengths of the numerical arguments for the other functions.

Examples

# Load necessary tools
data("fit_US_cities")
library(tidyverse)
x <- rcombdist(
  n = 25359, dist = "lnorm",
  prior = subset(fit_US_cities, (dist == "lnorm" & components == 5))$prior[[1]],
  coeff = subset(fit_US_cities, (dist == "lnorm" & components == 5))$coefficients[[1]]
) # Generate data from one of the fitted functions

# Evaluate functioning of dcomdist by calculating log likelihood for all distributions
loglike <- fit_US_cities %>%
  group_by(dist, components, np, n) %>%
  do(loglike = sum(dcombdist(dist = .[["dist"]], x = sort(x), prior = .[["prior"]][[1]],
  coeff = .[["coefficients"]][[1]], log = TRUE))) %>%
  unnest(cols = loglike) %>%
  mutate(NLL = -loglike, AIC = 2 * np - 2 * (loglike), BIC = log(n) * np - 2 * (loglike)) %>%
  arrange(NLL)

# Evaluate functioning of mcombdist and pcombdist by calculating NMAD
#(equivalent to the Kolmogorov-Smirnov test statistic for the zeroth moment
#of the distribution) for all distributions
nmad <- fit_US_cities %>%
  group_by(dist, components, np, n) %>%
  do(
    KS = max(abs(pempirical(q = sort(x), data = x) - pcombdist(dist = .[["dist"]],
    q = sort(x), prior = .[["prior"]][[1]], coeff = .[["coefficients"]][[1]]))),
    nmad_0 = nmad_test(r = 0, dist = .[["dist"]], x = sort(x), prior = .[["prior"]][[1]],
    coeff = .[["coefficients"]][[1]], stat = "max"),
    nmad_1 = nmad_test(r = 1, dist = .[["dist"]], x = sort(x), prior = .[["prior"]][[1]],
    coeff = .[["coefficients"]][[1]], stat = "max")
  ) %>%
  unnest(cols = c(KS, nmad_0, nmad_1)) %>%
  arrange(nmad_0)

# Evaluate functioning of qcombdist pcombdist by calculating NMAD (equivalent to the Kolmogorov-
#Smirnov test statistic for the zeroth moment of the distribution) for all distributions
test <- fit_US_cities %>%
  group_by(dist, components, np, n) %>%
  do(out = qcombdist(pcombdist(2, dist = .[["dist"]], prior = .[["prior"]][[1]],
  coeff = .[["coefficients"]][[1]], log.p = TRUE),
    dist = .[["dist"]], prior = .[["prior"]][[1]], coeff = .[["coefficients"]][[1]],
    log.p = TRUE
  )) %>%
  unnest(cols = c(out))