F_gam_mix: Mixture of two gamma distributions and related equilibrium...

In ARPobservation: Tools for Simulating Direct Behavioral Observation Recording Procedures Based on Alternating Renewal Processes

Mixture of two gamma distributions and related equilibrium distribution

Description

Random number generation from a mixture of two gamma distributions and the related equilibrium distribution, for use with r_behavior_stream.

Usage

F_gam_mix(shape1, shape2, scale_ratio, mix)

Arguments

shape1	shape parameter for first mixture component, k_1
shape2	shape parameter for second mixture component, k_2
scale_ratio	ratio of first scale component to second scale component, \theta_1 / \theta_2
mix	mixing proportion of first component, p

Value

Object of class eq_dist with components r_gen and r_eq.

The function r_gen(n, mean) generates random deviates from a mixture of two gamma distributions with specified mean, shape1, shape2, scale_ratio, and mix. The cumulative distribution function is given by

F(x) = p \Gamma(x; k_1, \theta_1) + (1 - p) \Gamma(x; k_2, \theta_2),

where \Gamma(x; k, \theta) is the cumulative distribution function of a Gamma random variable with shape k and scale \theta, and the scale parameters are determined by the specified mean and scale_ratio.

The function r_eq(n, mean) generates random deviates from the equilibrium distribution corresponding to the mixture of gamma distributions.

Examples

hist(F_gam_mix(2, 2, 1 / 12, 3 / 5)$r_gen(1000, 20))
hist(F_gam_mix(2, 2, 1 / 12, 3 / 5)$r_eq(1000, 20))

ARPobservation documentation built on Aug. 25, 2023, 5:19 p.m.