[rand.dist.bern.geo]

A geometric_distribution random number distribution produces integer values

i \geq 0

distributed according to the discrete probability function

P (i | p) = p \cdot (1 - p)^{i} .

template<class IntType = int>
  class geometric_distribution {
  public:
    // types
    using result_type = IntType;
    using param_type  = unspecified;

    // constructors and reset functions
    geometric_distribution() : geometric_distribution(0.5) {}
    explicit geometric_distribution(double p);
    explicit geometric_distribution(const param_type& parm);
    void reset();

    // generating functions
    template<class URBG>
      result_type operator()(URBG& g);
    template<class URBG>
      result_type operator()(URBG& g, const param_type& parm);

    // property functions
    double p() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };