discgammagpd: The discrete gamma-GPD spliced threshold distribution

In powerTCR: Model-Based Comparative Analysis of the TCR Repertoire

Description

Density, distribution function, quantile function and random generation for the discrete gamma-GPD spliced threshold distribution. The distribution has gamma bulk with shape equal to shape and rate equal to rate. It is spliced at a threshold equal to u and has a GPD tail with sigma equal to sigma and xi equal to xi. The proportion of data above the threshold phi is equal to phiu and the data are shifted according to shift.

Usage

ddiscgammagpd(x, fit, shape, rate, u, sigma, xi, phiu = NULL, shift = 0, log = FALSE)
pdiscgammagpd(q, fit, shape, rate, u, sigma, xi, phiu = NULL, shift = 0)
qdiscgammagpd(p, fit, shape, rate, u, sigma, xi, phiu = NULL, shift = 0)
rdiscgammagpd(n, fit, shape, rate, u, sigma, xi, phiu = NULL, shift = 0)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations.
fit	A fit output from fdiscgammagpd. If this object is passed, all parameter fields will automatically populate with the maximum likelihood estimates for the parameters in fit.
shape	shape parameter alpha of the truncated gamma distribution.
rate	rate parameter beta of the gamma distribution.
u	threshold.
sigma	scale parameter sigma of the GPD.
xi	shape parameter xi of the GPD
phiu	Propotion of data greater than or equal to threshold u.
shift	value the complete distribution is shifted by. Ideally, this is the smallest value of the count data from one sample.
log	Logical; if TRUE, probabilities p are given as log(p).

Details

The shape, rate, u, sigma, and xi parameters must be specified by the user. If phiu is left unspecified, it defaults to 1 minus the distribution function of a discrete gamma distribution (not a discrete truncated gamma) evaluated at u-1.

Value

ddiscgammagpd gives the density, pdiscgammagpd gives the distribution function, qdiscgammagpd gives the quantile function, and rdiscgammagpd generates random variables from the described distribution.

Author(s)

[e-mail]

Examples

# Generate and sort a random sample for a log-log plot
d <- rdiscgammagpd(100, shape = 5, rate = .25, u = 25,
                    sigma = 15, xi = .5, shift = 1)
d <- sort(d, decreasing = TRUE)
plot(log(d), log(1:100))

# When phiu is specified to .2, exactly 80%
# of the data are below the threshold u
pdiscgammagpd(24, shape = 5, rate = .25, u = 25,
                sigma = 15, xi = .5, phiu = .2, shift = 1)

# Plot simulated data versus theoretical quantiles
quantiles <- qdiscgammagpd((100:1)/101, shape = 5, rate = .25, u = 25,
                            sigma = 15, xi = .5, shift = 1)
plot(log(d), log(quantiles))
abline(0,1) # The line x=y

# Density below shift value should be 0
ddiscgammagpd(0, shape = 5, rate = .25, u = 25, sigma = 15, xi = .5, shift = 1)

# This is an example of using the "fit" input instead of manually specifying all parameters
data("repertoires")
thresholds1 <- unique(round(quantile(repertoires[[1]], c(.75,.8,.85,.9,.95))))
fit1 <- fdiscgammagpd(repertoires[[1]], useq = thresholds1, shift = min(repertoires[[1]]))
qdiscgammagpd(.6, fit1)

powerTCR documentation built on March 17, 2021, 6:01 p.m.