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19.2 Beta proportion distribution

19.2.1 Probability density function

If μ(0,1) and κR+, then for θ(0,1), Beta_Proportion(θ|μ,κ)=1B(μκ,(1μ)κ)θμκ1(1θ)(1μ)κ1, where the beta function B() is as defined in section combinatorial functions.

Warning: If θ=0 or θ=1, then the probability is 0 and the log probability is . Similarly, the distribution requires μ(0,1) and strictly positive parameter, κ>0.

19.2.2 Sampling statement

theta ~ beta_proportion(mu, kappa)

Increment target log probability density with beta_proportion_lupdf(theta | mu, kappa).

19.2.3 Stan functions

real beta_proportion_lpdf(reals theta | reals mu, reals kappa)
The log of the beta_proportion density of theta in (0,1) given mean mu and precision kappa

real beta_proportion_lupdf(reals theta | reals mu, reals kappa)
The log of the beta_proportion density of theta in (0,1) given mean mu and precision kappa dropping constant additive terms

real beta_proportion_lcdf(reals theta | reals mu, reals kappa)
The log of the beta_proportion cumulative distribution function of theta in (0,1) given mean mu and precision kappa

real beta_proportion_lccdf(reals theta | reals mu, reals kappa)
The log of the beta_proportion complementary cumulative distribution function of theta in (0,1) given mean mu and precision kappa

R beta_proportion_rng(reals mu, reals kappa)
Generate a beta_proportion variate with mean mu and precision kappa; may only be used in transformed data and generated quantities blocks. For a description of argument and return types, see section vectorized PRNG functions.