Statistics

Classes
class	Histogram
	Constructs and maintains a histogram of input data. More...
class	LeastSqFit
	Constructs a linear least squares fit to a straight line from input data. More...
class	RWRandGenBasicMLC
	Abstract base class for classes that generate random numbers uniformly distributed over the interval [0,1]. More...
class	RWRandGenerator
	Generates random numbers uniformly distributed over the interval [0, 1]. More...
class	RWRandGenMCG31M1
	Generates random numbers uniformly distributed over the interval [0, 1]. More...
class	RWRandGenMCG59
	Generates random numbers uniformly distributed over the interval [0, 1]. More...
class	RWRandGenMRG32K3A
	Generates random numbers uniformly distributed over the interval [0, 1]. More...
class	RWRandGenMTwist
	Generates random numbers uniformly distributed over the interval [0, 1]. More...
class	RWRandGenR250
	Generates random numbers uniformly distributed over the interval [0, 1]. More...
class	RWRandInterface
	Abstract base class for RWTRand. More...
class	RWTRand< Generator >
	Abstract base class from which the random number generator classes derive. More...
class	RWTRandBinomial< Generator >
	Used to generate random numbers from a binomial distribution. More...
class	RWTRandExponential< Generator >
	Used to generate random numbers from an exponential distribution. More...
class	RWTRandGamma< Generator >
	Used to generate random numbers from a gamma distribution. More...
class	RWTRandNormal< Generator >
	Used to generate random numbers from a normal distribution. More...
class	RWTRandPoisson< Generator >
	Used to generate random numbers from a Poisson distribution. More...
class	RWTRandUniform< Generator >
	Used to generate random numbers from a uniform distribution in an interval [a, b]. More...

Functions
double	beta (double w, double z)
double	binomialPF (size_t m, size_t N, double p)
double	exponentialPF (double x, double a)
double	factorial (size_t n)
double	gaussianPF (double x, double m, double s)
double	logGamma (double x)
double	lorentzianPF (double x, double m, double w)
double	poissonPF (size_t n, double m)
double	rwEpslon (double x)

Detailed Description

The Essential Math Statistics classes provide random number generators for a variety of probability distributions.

Function Documentation

beta()

double beta	(	double	w,
		double	z )

Header File

#include <rw/dstats.h>

Returns the Beta function:

\[ Beta(z,w) = \int\limits_0^1t^{z-1}(1-t)^{w-1}dt \]

binomialPF()

double binomialPF	(	size_t	m,
		size_t	N,
		double	p )

Header File

#include <rw/dstats.h>

The function binomialPF() returns the binomial probability coefficient. If an event has a probability p of occurring and we make N tries, binomialPF() returns the probability that the event will occur m times:

\[ \frac{N!}{(N-m)!m!}p^m(1-p)^{N-m} \]

exponentialPF()

double exponentialPF	(	double	x,
		double	a )

Header File

#include <rw/dstats.h>

Returns the exponential probability function. The quantity x / a has the probability distribution a exp(-ax).

factorial()

double factorial ( size_t n )

inline

Header File

#include <rw/dstats.h>

Returns the factorial of n, which is written n!. Stores previously calculated factorials internally for speed.

gaussianPF()

double gaussianPF	(	double	x,
		double	m,
		double	s )

Header File

#include <rw/dstats.h>

Returns the Gaussian probability function for Gaussian mean m and standard deviation s:

\[ \text{Z}(x) = \frac{1}{s\sqrt{2\pi}} \exp \left ( \frac{(x-m)^2}{2s^2} \right ) \]

logGamma()

double logGamma

(

double

x

)

Header File

#include <rw/dstats.h>

Returns the natural log of the gamma function \( \Gamma(x) \), where:

\[ \Gamma (x) = \int_{0}^{\infty} \text{t}^{x-1} \text{e}^{-t} \text{dt} \]

lorentzianPF()

double lorentzianPF	(	double	x,
		double	m,
		double	w )

Header File

#include <rw/dstats.h>

Returns the Lorentzian probability function, where m is the mean of the distribution and w is the full width at half maximum of the distribution.

poissonPF()

double poissonPF	(	size_t	n,
		double	m )

Header File

#include <rw/dstats.h>

The Poisson distribution gives the probability of a certain integer number of unit rate Poisson random events occurring in a given time interval. The Poisson distribution represents an approximation to the binomial distribution for the special case where the average number of events is very much smaller than the possible number. The function poissonPF() returns the probability that a Poisson random event with Poisson mean m will occur, given n observations:

\[ \frac{m^n e}{n!} \frac{m^n e^{-m}}{n!} \]

rwEpslon()

double rwEpslon

(

double

x

)

Header File

#include <rw/dstats.h>

Returns an estimate of the machine roundoff error in units of x, typically 1. This is frequently used to determine whether a number is near 0 relative to other numbers of order x.