[rand.dist] - C++11 → C++14

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tmp/tmpi8ullemh/{from.md → to.md} +8 -10

tmp/tmpi8ullemh/{from.md → to.md} RENAMED Viewed

@@ -205,11 +205,11 @@ constructed.
 A `binomial_distribution` random number distribution produces integer
 values i ≥ 0 distributed according to the discrete probability function
 $$%
  P(i\,|\,t,p)
-      = {t \choose i} \cdot p^i \cdot (1-p)^{t-i}
 \; \mbox{.}$$
 ``` cpp
 template<class IntType = int>
  class binomial_distribution
@@ -321,11 +321,11 @@ constructed.
 A `negative_binomial_distribution` random number distribution produces
 random integers i ≥ 0 distributed according to the discrete probability
 function $$%
  P(i\,|\,k,p)
-      = {k+i-1 \choose i} \cdot p^k \cdot (1-p)^i
 \; \mbox{.}$$
 ``` cpp
 template<class IntType = int>
  class negative_binomial_distribution
@@ -495,13 +495,11 @@ constructed.
 A `gamma_distribution` random number distribution produces random
 numbers x > 0 distributed according to the probability density function
 $$%
  p(x\,|\,\alpha,\beta)
-      = { e^{-x/\beta}
-        \over {\beta^{\alpha} \cdot \Gamma(\alpha)}
-        }
         \, \cdot \, x^{\, \alpha-1}
 \; \mbox{.}$$
 ``` cpp
 template<class RealType = double>
@@ -575,11 +573,11 @@ public:
  // types
  typedef RealType result_type;
  typedef unspecified param_type;
  // constructor and reset functions
- explicit weibull_distribution(RealType a = 1.0, RealType b = 1.0)
  explicit weibull_distribution(const param_type& parm);
  void reset();
  // generating functions
  template<class URNG>
@@ -690,11 +688,11 @@ constructed.
 ##### Class template `normal_distribution` <a id="rand.dist.norm.normal">[[rand.dist.norm.normal]]</a>
 A `normal_distribution` random number distribution produces random
 numbers x distributed according to the probability density function $$%
  p(x\,|\,\mu,\sigma)
-      = {1 \over \sigma \sqrt{2\pi}}
         \cdot
         % e^{-(x-\mu)^2 / (2\sigma^2)}
         \exp{\left(- \, \frac{(x - \mu)^2}
                              {2 \sigma^2}
              \right)
@@ -1184,11 +1182,11 @@ $$%
 The n+1 distribution parameters bᵢ, also known as this distribution’s
 *interval boundaries* , shall satisfy the relation bᵢ < bᵢ₊₁ for
 i = 0, …, n-1. Unless specified otherwise, the remaining n distribution
 parameters are calculated as: $$%
  \rho_k = \;
-   {w_k \over {S \cdot (b_{k+1}-b_k)}}
    \; \mbox{ for } k = 0, \ldots, n\!-\!1,$$ in which the values wₖ,
 commonly known as the *weights* , shall be non-negative, non-NaN, and
 non-infinity. Moreover, the following relation shall hold:
 0 < S = w₀ + ⋯ + wₙ₋₁.
@@ -1312,12 +1310,12 @@ k = 0, …, n-1.
 A `piecewise_linear_distribution` random number distribution produces
 random numbers x, b₀ ≤ x < bₙ, distributed over each subinterval
 [ bᵢ, bᵢ₊₁ ) according to the probability density function $$%
  p(x\,|\,b_0,\ldots,b_n,\;\rho_0,\ldots,\rho_n)
-      = \rho_i     \cdot {{b_{i+1} - x} \over {b_{i+1} - b_i}}
-      + \rho_{i+1} \cdot {{x - b_i} \over {b_{i+1} - b_i}}
 \; \mbox{,}
 \mbox{ for } b_i \le x < b_{i+1}
 \; \mbox{.}$$
 The n+1 distribution parameters bᵢ, also known as this distribution’s

 A `binomial_distribution` random number distribution produces integer
 values i ≥ 0 distributed according to the discrete probability function
 $$%
  P(i\,|\,t,p)
+      = \binom{t}{i} \cdot p^i \cdot (1-p)^{t-i}
 \; \mbox{.}$$
 ``` cpp
 template<class IntType = int>
  class binomial_distribution
 A `negative_binomial_distribution` random number distribution produces
 random integers i ≥ 0 distributed according to the discrete probability
 function $$%
  P(i\,|\,k,p)
+      = \binom{k+i-1}{i} \cdot p^k \cdot (1-p)^i
 \; \mbox{.}$$
 ``` cpp
 template<class IntType = int>
  class negative_binomial_distribution
 A `gamma_distribution` random number distribution produces random
 numbers x > 0 distributed according to the probability density function
 $$%
  p(x\,|\,\alpha,\beta)
+      = \frac{e^{-x/\beta}}{\beta^{\alpha} \cdot \Gamma(\alpha)}
         \, \cdot \, x^{\, \alpha-1}
 \; \mbox{.}$$
 ``` cpp
 template<class RealType = double>
  // types
  typedef RealType result_type;
  typedef unspecified param_type;
  // constructor and reset functions
+ explicit weibull_distribution(RealType a = 1.0, RealType b = 1.0);
  explicit weibull_distribution(const param_type& parm);
  void reset();
  // generating functions
  template<class URNG>
 ##### Class template `normal_distribution` <a id="rand.dist.norm.normal">[[rand.dist.norm.normal]]</a>
 A `normal_distribution` random number distribution produces random
 numbers x distributed according to the probability density function $$%
  p(x\,|\,\mu,\sigma)
+      = \frac{1}{\sigma \sqrt{2\pi}}
         \cdot
         % e^{-(x-\mu)^2 / (2\sigma^2)}
         \exp{\left(- \, \frac{(x - \mu)^2}
                              {2 \sigma^2}
              \right)
 The n+1 distribution parameters bᵢ, also known as this distribution’s
 *interval boundaries* , shall satisfy the relation bᵢ < bᵢ₊₁ for
 i = 0, …, n-1. Unless specified otherwise, the remaining n distribution
 parameters are calculated as: $$%
  \rho_k = \;
+ \frac{w_k}{S \cdot (b_{k+1}-b_k)}
    \; \mbox{ for } k = 0, \ldots, n\!-\!1,$$ in which the values wₖ,
 commonly known as the *weights* , shall be non-negative, non-NaN, and
 non-infinity. Moreover, the following relation shall hold:
 0 < S = w₀ + ⋯ + wₙ₋₁.
 A `piecewise_linear_distribution` random number distribution produces
 random numbers x, b₀ ≤ x < bₙ, distributed over each subinterval
 [ bᵢ, bᵢ₊₁ ) according to the probability density function $$%
  p(x\,|\,b_0,\ldots,b_n,\;\rho_0,\ldots,\rho_n)
+      = \rho_i     \cdot {\frac{b_{i+1} - x}{b_{i+1} - b_i}}
+      + \rho_{i+1} \cdot {\frac{x - b_i}{b_{i+1} - b_i}}
 \; \mbox{,}
 \mbox{ for } b_i \le x < b_{i+1}
 \; \mbox{.}$$
 The n+1 distribution parameters bᵢ, also known as this distribution’s

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