g_cdf: Cumulative distribution function (CDF)-based transformation

In drkowal/rSTAR: MCMC and EM algorithms for Simultaneous Transformation and Rounding (STAR) Models

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-Binimial 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)

drkowal/rSTAR documentation built on July 5, 2023, 2:18 p.m.