MDD Class Reference

Modify Distrete Distribution. More...

#include <qle/math/discretedistribution.hpp>

Static Public Member Functions
static DiscreteDistribution	convolve (const DiscreteDistribution &a, const DiscreteDistribution &b, Size buckets)
static DiscreteDistribution	rebucketfixednumber (const DiscreteDistribution &a, Size buckets)
static DiscreteDistribution	rebucketfixedstep (const DiscreteDistribution &a, Real step)
static DiscreteDistribution	sum (const DiscreteDistribution &a, const DiscreteDistribution &b, Size buckets)
static DiscreteDistribution	sumspecialunsorted (const DiscreteDistribution &a, const DiscreteDistribution &b, Real c)
static DiscreteDistribution	sumspecial (const DiscreteDistribution &a, const DiscreteDistribution &b, Real c)
static DiscreteDistribution	sumspecialright (const DiscreteDistribution &a, const DiscreteDistribution &b, Real c)
static DiscreteDistribution	splicemezz (const DiscreteDistribution &a, const DiscreteDistribution &b, Real c)
static DiscreteDistribution	scalarmultprob (const DiscreteDistribution &a, const Real &b)
static DiscreteDistribution	scalarmultx (const DiscreteDistribution &a, const Real &b)
static DiscreteDistribution	scalarshiftx (const DiscreteDistribution &a, const Real &b)
static DiscreteDistribution	functionmax (const DiscreteDistribution &a, const Real &b)
template<class F >
static DiscreteDistribution	function (F &, const DiscreteDistribution &a)
static DiscreteDistribution	functionmin (const DiscreteDistribution &a, const Real &b)
static Real	expectation (const DiscreteDistribution &a)
static Real	stdev (const DiscreteDistribution &a)
static Real	leftstdev (const DiscreteDistribution &a)
static Real	print (const DiscreteDistribution &a, const ostringstream &o)
static Real	probabilitymatch (const DiscreteDistribution &a, const DiscreteDistribution &b, Real c, bool forward)
static Real	probabilitymatch (const DiscreteDistribution &a, const DiscreteDistribution &b, Real c)
	Probability matching with linear interpolation.

Detailed Description

Modify Distrete Distribution.

This class implements a set of operations on discrete disctributions, that involve one or two distributions.

Member Function Documentation

convolve()

static DiscreteDistribution convolve ( const DiscreteDistribution &  a, const DiscreteDistribution &  b, Size  buckets  )

static

Convolution of two discrete distribution

rebucketfixednumber()

static DiscreteDistribution rebucketfixednumber ( const DiscreteDistribution &  a, Size  buckets  )

static

Amend the discretization of the distribution such that the number of buckets is reduced to the given number.

rebucketfixedstep()

static DiscreteDistribution rebucketfixedstep ( const DiscreteDistribution &  a, Real  step  )

static

Amend the discretization of the distribution such that the distance of adjacent buckets is reduced to the given number.

sum()

static DiscreteDistribution sum ( const DiscreteDistribution &  a, const DiscreteDistribution &  b, Size  buckets  )

static

Add two discrete distributions while introducing a desired number of buckets.

sumspecialunsorted()

static DiscreteDistribution sumspecialunsorted ( const DiscreteDistribution &  a, const DiscreteDistribution &  b, Real  c  )

static

Add c * distribution b to distribution a, starting from the left.

sumspecial()

static DiscreteDistribution sumspecial ( const DiscreteDistribution &  a, const DiscreteDistribution &  b, Real  c  )

static

Add c * distribution b to distribution a, starting from the right.

sumspecialright()

static DiscreteDistribution sumspecialright ( const DiscreteDistribution &  a, const DiscreteDistribution &  b, Real  c  )

static

TODO

splicemezz()

static DiscreteDistribution splicemezz ( const DiscreteDistribution &  a, const DiscreteDistribution &  b, Real  c  )

static

TODO

scalarmultprob()

static DiscreteDistribution scalarmultprob ( const DiscreteDistribution &  a, const Real &  b  )

static

Scale each density by factor b.

scalarmultx()

static DiscreteDistribution scalarmultx ( const DiscreteDistribution &  a, const Real &  b  )

static

Scale each coordinate by factor x.

scalarshiftx()

static DiscreteDistribution scalarshiftx ( const DiscreteDistribution &  a, const Real &  b  )

static

Shift each coordinate by amount b.

functionmax()

static DiscreteDistribution functionmax ( const DiscreteDistribution &  a, const Real &  b  )

static

CHECK: Cut off the branch of the distribution to the left of coordinate b and subsitute it with a single oint at coordinate b holding the cumulative probability up to b.

function()

DiscreteDistribution function ( F &  f, const DiscreteDistribution &  a  )

static

Apply function F to each coordinate.

functionmin()

static DiscreteDistribution functionmin ( const DiscreteDistribution &  a, const Real &  b  )

static

TODO

expectation()

static Real expectation ( const DiscreteDistribution &  a )

static

Return the expected coordinate value.

stdev()

static Real stdev ( const DiscreteDistribution &  a )

static

Return the standard deviation of the discrete distribution.

leftstdev()

static Real leftstdev ( const DiscreteDistribution &  a )

static

TODO

print()

static Real print ( const DiscreteDistribution &  a, const ostringstream &  o  )

static

Print the distribution the the provided stream.

probabilitymatch()

static Real probabilitymatch ( const DiscreteDistribution &  a, const DiscreteDistribution &  b, Real  c, bool  forward  )

static

Probability matching:

Compute the cumulative probability P_b(c) of distribution b up to the provided coordintae c.

Compute the coordinate c* of distribution a where its cumulative probability equals P_b(c), i.e. P_a(c*) = P_b(c).

Return coordinate c*.