Non-Parametric Cdf

A non-parametric cdf of variable Z is a cdf F defined by a discrete set of points $\Big($z_i, F(z_i)$\Big)$, i = 1,..., n. If variable Z is categorical, the z_i are all the possible values of Z, and the points $\Big($z_i, F(z_i)$\Big)$ fully describe the cdf of Z.

If on the other hand Z is a continuous variable, the points $\Big($z_i, F(z_i)$\Big)$ must be interpolated in order to associate a probability to any z-value.

Associated Types

• Value Type

  A::value_type

  The type of z (see definition above).

• Z-iterator

  A::z_iterator

  The type of the iterator to the values z₁,..., z_n (see definition above). A z-iterator is a model of Random-Access Iterator (as defined by STL).

• Z-iterator

  A::p_iterator

  The type of the iterator to the values p₁,..., z_n (see definition above). A p-iterator is a model of Random-Access Iterator (as defined by STL).

Refinement of

CDF, Default Constructitble

Notations

A		A type that is a model of Cdf
a		Object of type X
m		object of type unsigned int

Valid Expressions

• Resize

  a.resize(m)

  Return type:		void
  Semantics:		Redefines the size of the discretizations z1,..., zn and p1,..., zn. Space for m values is allocated.

• Size

  a.size()

  Return type:		int
  Semantics:		Returns the size of the discretization: n

• Access to the beginning of the z-set

  a.z_begin()

  Return type:		z_iterator
  Semantics:		provides an iterator to the zi's

• Access to the end of the z-set

  a.z_end()

  Return type:		z_iterator
  Semantics:		provides an iterator to the zi's

• Access to the beginning of the p-set

  a.p_begin()

  Return type:		p_iterator
  Semantics:		provides an iterator to the pi's

• Access to the end of the p-set

  a.p_end()

  Return type:		p_iterator
  Semantics:		provides an iterator to the pi's