Stan functions for working with the unifed distribution

A script with stan functions of the unifed is provided. The script
can be included in stan code. The full path to the script can be
obtained with the function `unifed.stan.path`

. The
following list are the names of functions that take one real value:

`real unifed_kappa(real theta)`

Computes the cumulant generator of the unifed distribution.

`real unifed_kappa_prime(real theta)`

Computes the first derivative of the cumulant generator.

`real unifed_kappa_double_prime(real theta)`

Computes the second derivative of the cumulant generator.

`real unifed_lpdf(real x,real theta)`

Computes the logarithm of the probability density function of a unifed distribution.

`theta`

is the value of the canonical parameter of the unifed and`x`

if the value where the density is evaluated.`real unifed_quantile(real p,real theta)`

Returns the p-th quantile of a unifed distribution with canonical parameter

`theta`

.

`real unifed_rng(real theta)`

Returns a simulated value of a unifed distribution with canonical parameter

`theta`

.`real unifed_lcdf(real x,real theta)`

Computes the logarithm of the cumulative density function of a unifed distribution.

`theta`

is the value of the canonical parameter of the unifed and`x`

if the value where the density is evaluated.`real unifed_kappa_prime_inverse(real mu)`

Returns the inverse of the derivative of the unifed cumulant generator

`real unifed_unit_deviance(real y,real mu)`

Unit deviance function of the unifed.

The following functions take vectors as arguments

`vector unifed_kappa_v(vector theta)`

Vectorized version of

`unifed_kappa`

.`vector unifed_kappa_prime_inverse_v(vector mu)`

Vectorized version of

`unifed_kappa_prime_inverse`

.`void unifed_glm_lp(vector y, vector theta, vector weights)`

Adds to the Log Probability Accumulator the logarithm of the likelihood function of a GLM with observed response

`y`

, estimated canonical parameter`theta`

and weights`weights`

.

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