g_cdf {countSTAR}

Cumulative distribution function (CDF)-based transformation

Description

Compute a CDF-based transformation using the observed count data. The CDF can be estimated nonparametrically or parametrically based on the Poisson or Negative Binomial distributions. In the parametric case, the parameters are determined based on the moments of y. Note that this is a fixed quantity and does not come with uncertainty quantification.

Usage

g_cdf(y, distribution = "np")

Arguments

y

n x 1 vector of observed counts

distribution

the distribution used for the CDF; must be one of

• "np" (empirical CDF)

• "pois" (moment-matched marginal Poisson CDF)

• "neg-bin" (moment-matched marginal Negative Binomial CDF)

Value

A smooth monotone function which can be used for evaluations of the transformation.

Examples

# Sample some data:
y = rpois(n = 500, lambda = 5)

# Empirical CDF version:
g_np = g_cdf(y, distribution = 'np')

# Poisson version:
g_pois = g_cdf(y, distribution = 'pois')

# Negative binomial version:
g_negbin = g_cdf(y, distribution = 'neg-bin')

# Plot together:
t = 1:max(y) # grid
plot(t, g_np(t), type='l')
lines(t, g_pois(t), lty = 2)
lines(t, g_negbin(t), lty = 3)