[rand.dist.samp]

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discrete_distribution();

Effects: Constructs a discrete_distribution object with

n = 1 and {p 0 = 1 .}_{0 = 1 .}

[Note 1:

Such an object will always deliver the value 0.

— end note]

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template<class InputIterator>
  discrete_distribution(InputIterator firstW, InputIterator lastW);

Mandates: is_convertible_v<iterator_traits<InputIterator>::value_type, double> is true.

Preconditions: InputIterator meets the Cpp17InputIterator requirements ([input.iterators]).

If firstW == lastW, let

n = 1 and {w 0 = 1 .}_{0 = 1 .}

Otherwise, [firstW, lastW) forms a sequence w of length

n > 0 .

Effects: Constructs a discrete_distribution object with probabilities given by the Formula 29.19 .

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discrete_distribution(initializer_list<double> wl);

Effects: Same as discrete_distribution(wl.begin(), wl.end().

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template<class UnaryOperation>
  discrete_distribution(size_t nw, double xmin, double xmax, UnaryOperation fw);

Preconditions: If

nw = 0, let n = 1, otherwise let n = nw .

The relation

0 < δ = (xmax - xmin) / n holds .

Effects: Constructs a discrete_distribution object with probabilities given by the formula above, using the following values: If

nw = 0, let {w 0 = 1 .}_{0 = 1 .}

Otherwise, let

{w k = fw (xmin + k \cdot δ + δ / 2) for k = 0, \dots, n - 1 .}_{k = fw (xmin + k \cdot δ + δ / 2) for k = 0, \dots, n - 1 .}

Complexity: The number of invocations of fw does not exceed n.

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vector<double> probabilities() const;

Returns: A vector<double> whose size member returns n and whose operator[] member returns

{p k when invoked with argument k for k = 0, \dots, n - 1 .}_{k when invoked with argument k for k = 0, \dots, n - 1 .}

29.5.9.6.2 Class template piecewise_constant_distribution [rand.dist.samp.pconst]

A piecewise_constant_distribution random number distribution produces random numbers x,

{b 0 \leq x < {b n, uniformly distributed over each subinterval [{b i, {b i + 1) according to the probability density function in Formula 29.20 .}_{i + 1) according to the probability density function in Formula 29.20 .}}_{i, {b i + 1) according to the probability density function in Formula 29.20 .}_{i + 1) according to the probability density function in Formula 29.20 .}}}_{n, uniformly distributed over each subinterval [{b i, {b i + 1) according to the probability density function in Formula 29.20 .}_{i + 1) according to the probability density function in Formula 29.20 .}}_{i, {b i + 1) according to the probability density function in Formula 29.20 .}_{i + 1) according to the probability density function in Formula 29.20 .}}}}_{0 \leq x < {b n, uniformly distributed over each subinterval [{b i, {b i + 1) according to the probability density function in Formula 29.20 .}_{i + 1) according to the probability density function in Formula 29.20 .}}_{i, {b i + 1) according to the probability density function in Formula 29.20 .}_{i + 1) according to the probability density function in Formula 29.20 .}}}_{n, uniformly distributed over each subinterval [{b i, {b i + 1) according to the probability density function in Formula 29.20 .}_{i + 1) according to the probability density function in Formula 29.20 .}}_{i, {b i + 1) according to the probability density function in Formula 29.20 .}_{i + 1) according to the probability density function in Formula 29.20 .}}}}

The

n + 1 distribution parameters {b i, also known as this distribution's interval boundaries, shall satisfy the relation {b i < {b i + 1 for i = 0, \dots, n - 1 .}_{i + 1 for i = 0, \dots, n - 1 .}}_{i < {b i + 1 for i = 0, \dots, n - 1 .}_{i + 1 for i = 0, \dots, n - 1 .}}}_{i, also known as this distribution's interval boundaries, shall satisfy the relation {b i < {b i + 1 for i = 0, \dots, n - 1 .}_{i + 1 for i = 0, \dots, n - 1 .}}_{i < {b i + 1 for i = 0, \dots, n - 1 .}_{i + 1 for i = 0, \dots, n - 1 .}}}

Unless specified otherwise, the remaining n distribution parameters are calculated as:

ρ {k = {w k S \cdot ({b k + 1 - {b k)}_{k)}}_{k + 1 - {b k)}_{k)}}}_{k S \cdot ({b k + 1 - {b k)}_{k)}}_{k + 1 - {b k)}_{k)}}}}_{k = {w k S \cdot ({b k + 1 - {b k)}_{k)}}_{k + 1 - {b k)}_{k)}}}_{k S \cdot ({b k + 1 - {b k)}_{k)}}_{k + 1 - {b k)}_{k)}}}}

Moreover, the following relation shall hold:

0 < S = {w 0 + \dots + {w n - 1 .}_{n - 1 .}}_{0 + \dots + {w n - 1 .}_{n - 1 .}}

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namespace std { template<class RealType = double> class piecewise_constant_distribution { public: / types using result_type = RealType; using param_type = unspecified; / constructor and reset functions piecewise_constant_distribution(); template<class InputIteratorB, class InputIteratorW> piecewise_constant_distribution(InputIteratorB firstB, InputIteratorB lastB, InputIteratorW firstW); template<class UnaryOperation> piecewise_constant_distribution(initializer_list<RealType> bl, UnaryOperation fw); template<class UnaryOperation> piecewise_constant_distribution(size_t nw, RealType xmin, RealType xmax, UnaryOperation fw); explicit piecewise_constant_distribution(const param_type& parm); void reset(); / equality operators friend bool operator=(const piecewise_constant_distribution& x, const piecewise_constant_distribution& y); / generating functions template<class URBG> result_type operator()(URBG& g); template<class URBG> result_type operator()(URBG& g, const param_type& parm); / property functions vector<result_type> intervals() const; vector<result_type> densities() const; param_type param() const; void param(const param_type& parm); result_type min() const; result_type max() const; / inserters and extractors template<class charT, class traits> friend basic_ostream<charT, traits>& operator<(basic_ostream<charT, traits>& os, const piecewise_constant_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>(basic_istream<charT, traits>& is, piecewise_constant_distribution& x); }; }

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piecewise_constant_distribution();

Effects: Constructs a piecewise_constant_distribution object with

n = 1, ρ {0 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}_{0 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}

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template<class InputIteratorB, class InputIteratorW>
  piecewise_constant_distribution(InputIteratorB firstB, InputIteratorB lastB,
                                  InputIteratorW firstW);

Mandates: Both of

(4.1)
is_convertible_v<iterator_traits<InputIteratorB>::value_type, double>
(4.2)
is_convertible_v<iterator_traits<InputIteratorW>::value_type, double>

are true.

Preconditions: InputIteratorB and InputIteratorW each meet the Cpp17InputIterator requirements ([input.iterators]).

If firstB == lastB or ++firstB == lastB, let

n = 1, {w 0 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}_{0 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}

Otherwise, [firstB, lastB) forms a sequence b of length

n + 1, the length of the sequence w starting from firstW is at least n, and any {w k for k \geq n are ignored by the distribution .}_{k for k \geq n are ignored by the distribution .}

Effects: Constructs a piecewise_constant_distribution object with parameters as specified above.

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template<class UnaryOperation>
  piecewise_constant_distribution(initializer_list<RealType> bl, UnaryOperation fw);

Effects: Constructs a piecewise_constant_distribution object with parameters taken or calculated from the following values: If

bl.size() < 2, let n = 1, {w 0 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}_{0 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}

Otherwise, let [bl.begin(), bl.end()) form a sequence

{b 0, \dots, {b n, and let {w k = fw (({b k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}_{k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}}_{k = fw (({b k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}_{k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}}}_{n, and let {w k = fw (({b k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}_{k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}}_{k = fw (({b k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}_{k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}}}}_{0, \dots, {b n, and let {w k = fw (({b k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}_{k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}}_{k = fw (({b k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}_{k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}}}_{n, and let {w k = fw (({b k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}_{k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}}_{k = fw (({b k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}_{k + 1 + {b k) / 2) for k = 0, \dots, n - 1 .}_{k) / 2) for k = 0, \dots, n - 1 .}}}}}

Complexity: The number of invocations of fw does not exceed n.

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template<class UnaryOperation>
  piecewise_constant_distribution(size_t nw, RealType xmin, RealType xmax, UnaryOperation fw);

Preconditions: If

nw = 0, let n = 1, otherwise let n = nw .

The relation

0 < δ = (xmax - xmin) / n holds .

Effects: Constructs a piecewise_constant_distribution object with parameters taken or calculated from the following values: Let

{b k = xmin + k \cdot δ for k = 0, \dots, n, and {w k = fw ({b k + δ / 2) for k = 0, \dots, n - 1 .}_{k + δ / 2) for k = 0, \dots, n - 1 .}}_{k = fw ({b k + δ / 2) for k = 0, \dots, n - 1 .}_{k + δ / 2) for k = 0, \dots, n - 1 .}}}_{k = xmin + k \cdot δ for k = 0, \dots, n, and {w k = fw ({b k + δ / 2) for k = 0, \dots, n - 1 .}_{k + δ / 2) for k = 0, \dots, n - 1 .}}_{k = fw ({b k + δ / 2) for k = 0, \dots, n - 1 .}_{k + δ / 2) for k = 0, \dots, n - 1 .}}}

Complexity: The number of invocations of fw does not exceed n.

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vector<result_type> intervals() const;

Returns: A vector<result_type> whose size member returns

n + 1 and whose operator [] member returns {b k when invoked with argument k for k = 0, \dots, n .}_{k when invoked with argument k for k = 0, \dots, n .}

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vector<result_type> densities() const;

Returns: A vector<result_type> whose size member returns n and whose operator[] member returns

ρ {k when invoked with argument k for k = 0, \dots, n - 1 .}_{k when invoked with argument k for k = 0, \dots, n - 1 .}

29.5.9.6.3 Class template piecewise_linear_distribution [rand.dist.samp.plinear]

A piecewise_linear_distribution random number distribution produces random numbers x,

{b 0 \leq x < {b n, distributed over each subinterval [{b i, {b i + 1) according to the probability density function in Formula 29.21 .}_{i + 1) according to the probability density function in Formula 29.21 .}}_{i, {b i + 1) according to the probability density function in Formula 29.21 .}_{i + 1) according to the probability density function in Formula 29.21 .}}}_{n, distributed over each subinterval [{b i, {b i + 1) according to the probability density function in Formula 29.21 .}_{i + 1) according to the probability density function in Formula 29.21 .}}_{i, {b i + 1) according to the probability density function in Formula 29.21 .}_{i + 1) according to the probability density function in Formula 29.21 .}}}}_{0 \leq x < {b n, distributed over each subinterval [{b i, {b i + 1) according to the probability density function in Formula 29.21 .}_{i + 1) according to the probability density function in Formula 29.21 .}}_{i, {b i + 1) according to the probability density function in Formula 29.21 .}_{i + 1) according to the probability density function in Formula 29.21 .}}}_{n, distributed over each subinterval [{b i, {b i + 1) according to the probability density function in Formula 29.21 .}_{i + 1) according to the probability density function in Formula 29.21 .}}_{i, {b i + 1) according to the probability density function in Formula 29.21 .}_{i + 1) according to the probability density function in Formula 29.21 .}}}}

The

n + 1 distribution parameters {b i, also known as this distribution's interval boundaries, shall satisfy the relation {b i < {b i + 1 for i = 0, \dots, n - 1 .}_{i + 1 for i = 0, \dots, n - 1 .}}_{i < {b i + 1 for i = 0, \dots, n - 1 .}_{i + 1 for i = 0, \dots, n - 1 .}}}_{i, also known as this distribution's interval boundaries, shall satisfy the relation {b i < {b i + 1 for i = 0, \dots, n - 1 .}_{i + 1 for i = 0, \dots, n - 1 .}}_{i < {b i + 1 for i = 0, \dots, n - 1 .}_{i + 1 for i = 0, \dots, n - 1 .}}}

Unless specified otherwise, the remaining

n + 1 distribution parameters are calculated as ρ {k = {w k / S for k = 0, \dots, n, in which the values {w k, commonly known as the weights at boundaries, shall be non-negative, non-NaN, and non-infinity .}_{k, commonly known as the weights at boundaries, shall be non-negative, non-NaN, and non-infinity .}}_{k / S for k = 0, \dots, n, in which the values {w k, commonly known as the weights at boundaries, shall be non-negative, non-NaN, and non-infinity .}_{k, commonly known as the weights at boundaries, shall be non-negative, non-NaN, and non-infinity .}}}_{k = {w k / S for k = 0, \dots, n, in which the values {w k, commonly known as the weights at boundaries, shall be non-negative, non-NaN, and non-infinity .}_{k, commonly known as the weights at boundaries, shall be non-negative, non-NaN, and non-infinity .}}_{k / S for k = 0, \dots, n, in which the values {w k, commonly known as the weights at boundaries, shall be non-negative, non-NaN, and non-infinity .}_{k, commonly known as the weights at boundaries, shall be non-negative, non-NaN, and non-infinity .}}}

Moreover, the following relation shall hold:

0 < S = \frac{12}{2}

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namespace std { template<class RealType = double> class piecewise_linear_distribution { public: / types using result_type = RealType; using param_type = unspecified; / constructor and reset functions piecewise_linear_distribution(); template<class InputIteratorB, class InputIteratorW> piecewise_linear_distribution(InputIteratorB firstB, InputIteratorB lastB, InputIteratorW firstW); template<class UnaryOperation> piecewise_linear_distribution(initializer_list<RealType> bl, UnaryOperation fw); template<class UnaryOperation> piecewise_linear_distribution(size_t nw, RealType xmin, RealType xmax, UnaryOperation fw); explicit piecewise_linear_distribution(const param_type& parm); void reset(); / equality operators friend bool operator=(const piecewise_linear_distribution& x, const piecewise_linear_distribution& y); / generating functions template<class URBG> result_type operator()(URBG& g); template<class URBG> result_type operator()(URBG& g, const param_type& parm); / property functions vector<result_type> intervals() const; vector<result_type> densities() const; param_type param() const; void param(const param_type& parm); result_type min() const; result_type max() const; / inserters and extractors template<class charT, class traits> friend basic_ostream<charT, traits>& operator<(basic_ostream<charT, traits>& os, const piecewise_linear_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>(basic_istream<charT, traits>& is, piecewise_linear_distribution& x); }; }

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piecewise_linear_distribution();

Effects: Constructs a piecewise_linear_distribution object with

n = 1, ρ {0 = ρ {1 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}_{1 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}}_{0 = ρ {1 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}_{1 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}}

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template<class InputIteratorB, class InputIteratorW>
  piecewise_linear_distribution(InputIteratorB firstB, InputIteratorB lastB,
                                InputIteratorW firstW);

Mandates: Both of

(4.1)
is_convertible_v<iterator_traits<InputIteratorB>::value_type, double>
(4.2)
is_convertible_v<iterator_traits<InputIteratorW>::value_type, double>

are true.

Preconditions: InputIteratorB and InputIteratorW each meet the Cpp17InputIterator requirements ([input.iterators]).

If firstB == lastB or ++firstB == lastB, let

n = 1, ρ {0 = ρ {1 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}_{1 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}}_{0 = ρ {1 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}_{1 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}}

Otherwise, [firstB, lastB) forms a sequence b of length

n + 1, the length of the sequence w starting from firstW is at least n + 1, and any {w k for k \geq n + 1 are ignored by the distribution .}_{k for k \geq n + 1 are ignored by the distribution .}

Effects: Constructs a piecewise_linear_distribution object with parameters as specified above.

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template<class UnaryOperation>
  piecewise_linear_distribution(initializer_list<RealType> bl, UnaryOperation fw);

Effects: Constructs a piecewise_linear_distribution object with parameters taken or calculated from the following values: If

bl.size() < 2, let n = 1, ρ {0 = ρ {1 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}_{1 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}}_{0 = ρ {1 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}_{1 = 1, {b 0 = 0, and {b 1 = 1 .}_{1 = 1 .}}_{0 = 0, and {b 1 = 1 .}_{1 = 1 .}}}}

Otherwise, let [bl.begin(), bl.end()) form a sequence

{b 0, \dots, {b n, and let {w k = fw ({b k) for k = 0, \dots, n .}_{k) for k = 0, \dots, n .}}_{k = fw ({b k) for k = 0, \dots, n .}_{k) for k = 0, \dots, n .}}}_{n, and let {w k = fw ({b k) for k = 0, \dots, n .}_{k) for k = 0, \dots, n .}}_{k = fw ({b k) for k = 0, \dots, n .}_{k) for k = 0, \dots, n .}}}}_{0, \dots, {b n, and let {w k = fw ({b k) for k = 0, \dots, n .}_{k) for k = 0, \dots, n .}}_{k = fw ({b k) for k = 0, \dots, n .}_{k) for k = 0, \dots, n .}}}_{n, and let {w k = fw ({b k) for k = 0, \dots, n .}_{k) for k = 0, \dots, n .}}_{k = fw ({b k) for k = 0, \dots, n .}_{k) for k = 0, \dots, n .}}}}

Complexity: The number of invocations of fw does not exceed

n + 1 .

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template<class UnaryOperation>
  piecewise_linear_distribution(size_t nw, RealType xmin, RealType xmax, UnaryOperation fw);

Preconditions: If

nw = 0, let n = 1, otherwise let n = nw .

The relation

0 < δ = (xmax - xmin) / n holds .

Effects: Constructs a piecewise_linear_distribution object with parameters taken or calculated from the following values: Let

{b k = xmin + k \cdot δ for k = 0, \dots, n, and {w k = fw ({b k) for k = 0, \dots, n .}_{k) for k = 0, \dots, n .}}_{k = fw ({b k) for k = 0, \dots, n .}_{k) for k = 0, \dots, n .}}}_{k = xmin + k \cdot δ for k = 0, \dots, n, and {w k = fw ({b k) for k = 0, \dots, n .}_{k) for k = 0, \dots, n .}}_{k = fw ({b k) for k = 0, \dots, n .}_{k) for k = 0, \dots, n .}}}

Complexity: The number of invocations of fw does not exceed

n + 1 .

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vector<result_type> intervals() const;

Returns: A vector<result_type> whose size member returns

n + 1 and whose operator [] member returns {b k when invoked with argument k for k = 0, \dots, n .}_{k when invoked with argument k for k = 0, \dots, n .}

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vector<result_type> densities() const;

Returns: A vector<result_type> whose size member returns n and whose operator[] member returns

ρ {k when invoked with argument k for k = 0, \dots, n .}_{k when invoked with argument k for k = 0, \dots, n .}