# fun_integ: Calculate the integrand for the marginal distribution of X... In tamustatsy/bcdd: Bayesian constrained density deconvolution

## Description

The (posterior) marginal distribution of X equals the integral of the conditional distribution of X given theta, uniform over [-theta, theta], weighted by the (posterior) distribution of theta, a mixture of Gammas. The function fun_integ explicitly computes the integrand as a function of theta.

## Usage

 `1` ```fun_integ(x, pi, shape, rate) ```

## Arguments

 `x` a number (vector) specifies the value of the domain argument. `pi` a vector containing the component probabilities of the Gammas `shape, ` rate numeric vectors corresponding to shape and rate parameters of Gammas

## Value

The (posterior) marginal distribution of X (over theta) at the input parameter x.

## Examples

 ```1 2 3 4 5 6 7``` ```pi <- c(0.2,0.5,0.3) shape <- c(2.3,3.3,4.3) rate <- c(1.5,2.5,3.5) theta <- 0.1 fun_integ(theta, pi, shape, rate) theta <- c(0.1,0.5,3) fun_integ(theta, pi, shape, rate) ```

tamustatsy/bcdd documentation built on May 7, 2019, 9:39 a.m.