marenv::calc::CumulativeDistribution Class Reference

#include <CumulativeDistribution.h>

Public Types
using	probabilityDensity = std::function< double(double)>
	Signature for functions used to define probability density functions.

Public Member Functions
	CumulativeDistribution (probabilityDensity pdf, double xMin, double xMax, int numBins)
double	ValueAtCumulativeProbability (double probability) const

Detailed Description

Cumulative distribution built from a probability density function (PDF) on a closed interval.

The interval \([x_{\min}, x_{\max}]\) is discretized into \(N\) uniform bins with width \(h = (x_{\max}-x_{\min})/N\). Let \(p_i \approx \int_{x_i}^{x_{i+1}} f(x)\,dx\) be the bin probability masses obtained by (e.g.) midpoint rule. The cumulative distribution is \(F_k = \sum_{i=0}^{k-1} p_i\) with \(F_0=0\) and \(F_N=1\) after normalization.

This class stores the cumulative (CDF) samples and supports efficient inverse lookup: for a given cumulative probability \(u \in [0,1]\), return the corresponding \(x\) (piecewise linear within a bin).

Constructor & Destructor Documentation

CumulativeDistribution()

marenv::calc::CumulativeDistribution::CumulativeDistribution	(	probabilityDensity	pdf,
		double	xMin,
		double	xMax,
		int	numBins
	)

Constructor.

Parameters

pdf	The probability density function.
xMin	The minimum x value.
xMax	The maximum x value.
numBins	The number of bins to use for the integration.

Member Function Documentation

ValueAtCumulativeProbability()

double marenv::calc::CumulativeDistribution::ValueAtCumulativeProbability

(

double

probability

)

const

Calculates the x value which has a certain cumulative probability.

Parameters

probability

Cumulative probability.

Returns

The corresponding x value.

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The documentation for this class was generated from the following file:

• /update_root/webfhsim/reloadrepos/marenv/include/marenv/calc/CumulativeDistribution.h