This class implements the hypoexponential distribution for the case of equidistant \(\lambda_i = (n+1-i)h\). More...

Inheritance diagram for HypoExponentialDistEqual:

Collaboration diagram for HypoExponentialDistEqual:

Public Member Functions
	HypoExponentialDistEqual (int n, int k, double h)
	Constructor for equidistant rates. More...

double	density (double x)

double	cdf (double x)
	Returns the distribution function \(F(x)\). More...

double	barF (double x)
	Returns \(\bar{F}(x) = 1 - F(x)\). More...

double	inverseF (double u)
	Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More...

double []	getParams ()
	Returns the three parameters of this hypoexponential distribution as array \((n, k, h)\). More...

void	setParams (int n, int k, double h)

String	toString ()

Public Member Functions inherited from HypoExponentialDist
	HypoExponentialDist (double[] lambda)
	Constructs a `HypoExponentialDist` object, with rates \(\lambda_i = \) `lambda[` \(i-1\)`]`, \(i = 1,…,k\). More...

double	density (double x)

double	cdf (double x)
	Returns the distribution function \(F(x)\). More...

double	barF (double x)
	Returns \(\bar{F}(x) = 1 - F(x)\). More...

double	inverseF (double u)
	Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More...

double	getMean ()
	Returns the mean of the distribution function.

double	getVariance ()
	Returns the variance of the distribution function.

double	getStandardDeviation ()
	Returns the standard deviation of the distribution function.

double []	getLambda ()
	Returns the values \(\lambda_i\) for this object.

void	setLambda (double[] lambda)
	Sets the values \(\lambda_i = \)`lambda[` \(i-1\)`]`, \(i = 1,…,k\) for this object.

double []	getParams ()
	Same as getLambda.

String	toString ()
	Returns a `String` containing information about the current distribution.

Public Member Functions inherited from ContinuousDistribution
abstract double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\). More...

double	barF (double x)
	Returns the complementary distribution function. More...

double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method. More...

double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection. More...

double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\). More...

double	getMean ()
	Returns the mean. More...

double	getVariance ()
	Returns the variance. More...

double	getStandardDeviation ()
	Returns the standard deviation. More...

double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

void	setXinf (double xa)
	Sets the value \(x_a=\) `xa`, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

void	setXsup (double xb)
	Sets the value \(x_b=\) `xb`, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

Static Public Member Functions
static double	density (int n, int k, double h, double x)
	Computes the density function \(f(x)\), with the same arguments as in the constructor. More...

static double	cdf (int n, int k, double h, double x)
	Computes the distribution function \(F(x)\), with arguments as in the constructor. More...

static double	barF (int n, int k, double h, double x)
	Computes the complementary distribution \(\bar{F}(x)\), as in formula ( conv-hypo-equal ). More...

static double	inverseF (int n, int k, double h, double u)
	Computes the inverse distribution \(x=F^{-1}(u)\), with arguments as in the constructor. More...

Static Public Member Functions inherited from HypoExponentialDist
static double	density (double[] lambda, double x)
	Computes the density function \(f(x)\), with \(\lambda_i = \) `lambda[` \(i-1\)`]`, \(i = 1,…,k\). More...

static double	cdf (double[] lambda, double x)
	Computes the distribution function \(F(x)\), with \(\lambda_i = \) `lambda[` \(i-1\)`]`, \(i = 1,…,k\). More...

static double	cdf2 (double[] lambda, double x)
	Computes the distribution function \(F(x)\), with \(\lambda_i = \) `lambda[` \(i-1\)`]`, \(i = 1,…,k\). More...

static double	barF (double[] lambda, double x)
	Computes the complementary distribution \(\bar{F}(x)\), with \(\lambda_i = \) `lambda[` \(i-1\)`]`, \(i = 1,…,k\). More...

static double	inverseF (double[] lambda, double u)
	Computes the inverse distribution function \(F^{-1}(u)\), with \(\lambda_i = \) `lambda[` \(i-1\)`]`, \(i = 1,…,k\). More...

static double	getMean (double[] lambda)
	Returns the mean, \(E[X] = \sum_{i=1}^k 1/\lambda_i\), of the hypoexponential distribution with rates \(\lambda_i = \) `lambda[` \(i-1\)`]`, \(i = 1,…,k\). More...

static double	getVariance (double[] lambda)
	Returns the variance, \(\mbox{Var}[X] = \sum_{i=1}^k 1/\lambda_i^2\), of the hypoexponential distribution with rates \(\lambda_i = \) `lambda[` \(i-1\)`]`, \(i = 1,…,k\). More...

static double	getStandardDeviation (double[] lambda)
	Returns the standard deviation of the hypoexponential distribution with rates \(\lambda_i = \) `lambda[` \(i-1\)`]`, \(i = 1,…,k\). More...

Additional Inherited Members
Public Attributes inherited from ContinuousDistribution
int	decPrec = 15

Static Protected Member Functions inherited from HypoExponentialDist
static void	testLambda (double[] lambda)

Protected Attributes inherited from HypoExponentialDist
double []	m_lambda

Protected Attributes inherited from ContinuousDistribution
double	supportA = Double.NEGATIVE_INFINITY

double	supportB = Double.POSITIVE_INFINITY

Static Protected Attributes inherited from ContinuousDistribution
static final double	XBIG = 100.0

static final double	XBIGM = 1000.0

static final double []	EPSARRAY

Detailed Description

This class implements the hypoexponential distribution for the case of equidistant \(\lambda_i = (n+1-i)h\).

We have \(\lambda_{i+1} - \lambda_i = h\), with \(h\) a constant, and \(n \ge k\) are integers.

The formula ( convolution-hypo ) becomes

\[ \bar{F}(x) = \mathbb P\left[X_1 + \cdots+ X_k > x \right] = \sum_{i=1}^k e^{-(n+1-i)h x} \prod_{\substack {j=1\\j\not i}}^k \frac{n+1-j}{i - j}. \tag{conv-hypo-equal} \]

The formula ( fhypoexp2 ) for the density becomes

\[ f(x) = \sum_{i=1}^k (n+1-i)h e^{-(n+1-i)h x} \prod_{\substack {j=1\\j\not i}}^k \frac{n+1-j}{i - j}. \tag{fhypoexp3} \]

Constructor & Destructor Documentation

◆ HypoExponentialDistEqual()

HypoExponentialDistEqual	(	int	n,
		int	k,
		double	h
	)

Constructor for equidistant rates.

The rates are \(\lambda_i = (n+1-i)h\), for \(i = 1,…,k\).

Parameters

n	largest rate is \(nh\)
k	number of rates
h	difference between adjacent rates

Member Function Documentation

◆ barF() [1/2]

double barF ( double x )

Returns \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Implements Distribution.

◆ barF() [2/2]

static double barF	(	int	n,
		int	k,
		double	h,
		double	x
	)

static

Computes the complementary distribution \(\bar{F}(x)\), as in formula ( conv-hypo-equal ).

Parameters

n	max possible number of \(\lambda_i\)
k	effective number of \(\lambda_i\)
h	step between two successive \(\lambda_i\)
x	value at which the complementary distribution is evaluated

Returns: value of complementary distribution at \(x\)

◆ cdf() [1/2]

double cdf ( double x )

Returns the distribution function \(F(x)\).

Parameters

x	value at which the distribution function is evaluated

Returns: distribution function evaluated at x

Implements Distribution.

◆ cdf() [2/2]

static double cdf	(	int	n,
		int	k,
		double	h,
		double	x
	)

static

Computes the distribution function \(F(x)\), with arguments as in the constructor.

Parameters

n	max possible number of \(\lambda_i\)
k	effective number of \(\lambda_i\)
h	step between two successive \(\lambda_i\)
x	value at which the distribution is evaluated

Returns: value of distribution at \(x\)

◆ density()

static double density	(	int	n,
		int	k,
		double	h,
		double	x
	)

static

Computes the density function \(f(x)\), with the same arguments as in the constructor.

Parameters

n	max possible number of \(\lambda_i\)
k	effective number of \(\lambda_i\)
h	step between two successive \(\lambda_i\)
x	value at which the distribution is evaluated

Returns: density at \(x\)

◆ getParams()

double [] getParams ( )

Returns the three parameters of this hypoexponential distribution as array \((n, k, h)\).

Returns: parameters of the hypoexponential distribution

Implements Distribution.

◆ inverseF() [1/2]

double inverseF ( double u )

Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ).

Parameters

u	value in the interval \((0,1)\) for which the inverse distribution function is evaluated

Returns: the inverse distribution function evaluated at u

Implements Distribution.

◆ inverseF() [2/2]

static double inverseF	(	int	n,
		int	k,
		double	h,
		double	u
	)

static

Computes the inverse distribution \(x=F^{-1}(u)\), with arguments as in the constructor.

Parameters

n	max possible number of \(\lambda_i\)
k	effective number of \(\lambda_i\)
h	step between two successive \(\lambda_i\)
u	value at which the inverse distribution is evaluated

Returns: inverse distribution at \(u\)

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

HypoExponentialDistEqual.java

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ HypoExponentialDistEqual()

Member Function Documentation

◆ barF() [1/2]

◆ barF() [2/2]

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ density()

◆ getParams()

◆ inverseF() [1/2]

◆ inverseF() [2/2]