update quantile function

closes #50

functions/inverse_cdf/johnson_quantile_icdf.stan → functions/quantile_function/johnson_qf.stan

@@ -1,14 +1,14 @@
-  /** @addtogroup johnson_quantile_icdf Johnson Quantile Parameterized Distributions (J-QPD) functions
+  /** @addtogroup johnson_qf Johnson Quantile Parameterized Distributions (J-QPD) functions
    *
    * Christopher C. Hadlock, J. Eric Bickel
    * The Generalized Johnson Quantile-Parameterized Distribution System. 
    * Decision Analysis 16 (1) 67-85 https://doi.org/10.1287/deca.2018.0376
    *
-   * \ingroup icdf
+   * \ingroup qf
    *  @{ */
 
   /**
-   *  Inverse CDF of the J-QPD-S semi-bounded distribution, which has moments
+   *  Quantile function of the J-QPD-S semi-bounded distribution, which has moments
    *
    * \f{aligned}{
    *      F^{-1}(p, l, x_\alpha) = 
@@ -45,7 +45,7 @@
    *  @throws reject if \f$ \alpha \notin [0, 1] \f$
    *  @throws reject if quantiles \f$ \ne 3\f$  
    */
-  real JQPDS_icdf(real p, real lower_bound, data real alpha, vector quantiles) {
+  real JQPDS_qf(real p, real lower_bound, data real alpha, vector quantiles) {
     if (p < 0 || p > 1)         reject("p must be between 0 and 1");
     if (alpha < 0 || alpha > 1) reject("alpha must be between 0 and 1");
     if (rows(quantiles) != 3)   reject("quantiles must have three elements");
@@ -88,7 +88,7 @@
   }
 
  /**
-  *   Inverse CDF of the J-QPD-S-II semi-bounded distribution, which lacks moments
+  *   Quantile function of the J-QPD-S-II semi-bounded distribution, which lacks moments
   *   
   * \f{aligned}{
    *      F^{-1}(p, l, x_\alpha) = 
@@ -124,7 +124,7 @@
    *  @throws reject if \f$ \alpha \notin [0, 1] \f$
    *  @throws reject if quantiles \f$ \ne 3\f$ 
    */
-  real JQPDS2_icdf(real p, real lower_bound, data real alpha, vector quantiles) {
+  real JQPDS2_qf(real p, real lower_bound, data real alpha, vector quantiles) {
     if (p < 0 || p > 1)         reject("p must be between 0 and 1");
     if (alpha < 0 || alpha > 1) reject("alpha must be between 0 and 1");
     if (rows(quantiles) != 3)   reject("quantiles must have three elements");
@@ -158,7 +158,7 @@
   }
 
   /**
-   * Inverse CDF of the J-QPD-B bounded distribution
+   * Quantile function of the J-QPD-B bounded distribution
    *   
    * \f{aligned}{
    *      F^{-1}(p, u, l, x_\alpha) = 
@@ -195,7 +195,7 @@
    * @throws reject if \f$ \alpha \notin [0, 1] \f$
    * @throws reject if quantiles \f$ != 3\f$ 
    */
-  real JQPDB_icdf(real p, row_vector bounds, data real alpha, vector quantiles) {
+  real JQPDB_qf(real p, row_vector bounds, data real alpha, vector quantiles) {
     if (cols(bounds) != 2)      reject("bounds must have two elements");
     if (bounds[2] == positive_infinity()) {
       return JQPDS2_icdf(p, alpha, bounds[1], quantiles);

functions/inverse_cdf/lognormal_icdf.stan → functions/quantile_function/lognormal_qf.stan

@@ -1,5 +1,5 @@
-  /** @ingroup icdf
-   * **Lognormal Inverse CDF**
+  /** @ingroup qf
+   * **Lognormal Quantile Function**
    * 
    * \f{aligned}{
    *  F^{-1}(p) &= \exp(\mu + \sqrt{2} \, \sigma \, \text{inv_erf}(2p - 1)) \\
@@ -20,7 +20,7 @@
    * @return inverse CDF value
    * @throws reject if \f$ p \notin [0, 1] \f$ 
    */
-real lognormal_icdf (real p, real mu, real sigma){
+real lognormal_qf (real p, real mu, real sigma){
    if (is_nan(p) || p < 0 || p > 1)
      reject("lognormal_icdf: p must be between 0 and 1; ",
            "found p = ", p);

functions/quantile_function/qf_definition.stan

@@ -0,0 +1,9 @@
+  /** \defgroup qf Quantile Functions also known as Inverse Cumulative Distribution Functions
+  *
+  * In probability and statistics, the quantile function - also known as  
+  * an inverse cumulative distribution function - is, associated with a probability distribution of a random variable, specifies 
+  * the value of the random variable such that the probability of the variable being less than or equal
+  * to that value equals the given probability.  
+  *
+  * See https://en.wikipedia.org/wiki/Quantile_function for more information.
+  **/

functions/inverse_cdf/skewed_generalized_t_icdf.stan → functions/quantile_function/skewed_generalized_t_qf.stan

@@ -1,7 +1,7 @@
 #include special/inc_beta_inverse.stan
 
-  /** @ingroup icdf
-   * Skewed generalized T inverse CDF
+  /** @ingroup qf
+   * Skewed Generalized T Quantile Function
    *
    * 
    * For more information, please see @ref skew_generalized_t.
@@ -16,7 +16,7 @@
    * @param q Real \f$\in (0, \infty)\f$ kurtosis parameter  
    * @return log probability
    */
- real skewed_generalized_t_icdf (real p, real mu, real sigma, real lambda, real p, real q) {
+ real skewed_generalized_t_qf (real p, real mu, real sigma, real lambda, real p, real q) {
     real z1 = beta(1.0 / p, q);
     real z2 = beta(2.0 / p, q - 1.0 / p);
     real v = sigma * q^(-1.0/p) * inv_sqrt( ( 3 * square(lambda) + 1 ) * beta(3.0/p, q - 2.0/p) / z1 - 4 * square(lambda * z2 / z1) );

functions/inverse_cdf/unit_johnson_su_icdf.stan → functions/quantile_function/unit_johnson_su_qf.stan

@@ -1,5 +1,5 @@
-  /** @ingroup icdf
-   * Unit Johnson SU Inverse CDF
+  /** @ingroup qf
+   * Unit Johnson SU Quantile Function
    * 
    * \f{aligned}{
    *  F^{-1}(p, \, \mu, \, \sigma) &= \text{inv_logit}\bigg[ \sinh\bigg(\frac{\Phi^{-1}(p) - \mu}{\sigma}\bigg) \bigg]\\
@@ -12,7 +12,7 @@
    * @return inverse CDF value
    * @throws reject if \f$ p \notin [0, 1] \f$ 
    */
-  real unit_johnson_icdf (real p, real mu, real sigma){
+  real unit_johnson_qf (real p, real mu, real sigma){
    if (is_nan(p) || p < 0 || p > 1)
      reject("unit_johnson_icdf: p must be between 0 and 1; ",
            "found p = ", p);