umontreal.iro.lecuyer.probdist
Class HypoExponentialDistEqual

java.lang.Object
  umontreal.iro.lecuyer.probdist.ContinuousDistribution
      umontreal.iro.lecuyer.probdist.HypoExponentialDist
          umontreal.iro.lecuyer.probdist.HypoExponentialDistEqual

All Implemented Interfaces:

Distribution

public class HypoExponentialDistEqual
extends HypoExponentialDist

This class implements the hypoexponential distribution for the case of equidistant λ_i = (n + 1 - i)h. We have λ_i+1 - λ_i = h, with h a constant, and n >= k are integers.

The formula becomes

bar(F)(x) = P[X₁ + ^... + X_k > x] = ∑_i=1^ke^-(n+1-i)hx∏_{j=1j i}^kn+1-j/i-j.

The formula for the density becomes

f (x) = ∑_i=1^k(n + 1 - i)he^-(n+1-i)hx∏_{[tex2html_wrap_indisplay193]j=1j [tex2html_wrap_indisplay194]i}^kn+1-j/i-j.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

decPrec

Constructor Summary

HypoExponentialDistEqual(int n, int k, double h)
Constructor for equidistant rates.

Method Summary

double	barF(double x) Returns the complementary distribution function.
static double	barF(int n, int k, double h, double x) Computes the complementary distribution bar(F)(x), as in formula.
double	cdf(double x) Returns the distribution function F(x).
static double	cdf(int n, int k, double h, double x) Computes the distribution function F(x), with arguments as in the constructor.
double	density(double x) Returns f (x), the density evaluated at x.
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.
double[]	getParams() Returns the three parameters of this hypoexponential distribution as array (n, k, h).
double	inverseF(double u) Returns the inverse distribution function x = F-1(u).
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.
void	setParams(int n, int k, double h)
String	toString()

Methods inherited from class umontreal.iro.lecuyer.probdist.HypoExponentialDist

barF, cdf, cdf2, density, getLambda, getMean, getMean, getStandardDeviation, getStandardDeviation, getVariance, getVariance, inverseF, setLambda

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

HypoExponentialDistEqual

public HypoExponentialDistEqual(int n,
                                int k,
                                double h)

Constructor for equidistant rates. The rates are λ_i = (n + 1 - i)h, for i = 1,…, k.

Parameters:

n - largest rate is nh

k - number of rates

h - difference between adjacent rates

Method Detail

density

public double density(double x)

Description copied from class: ContinuousDistribution

Returns f (x), the density evaluated at x.

Overrides:

density in class HypoExponentialDist

Parameters:

x - value at which the density is evaluated

Returns:

density function evaluated at x

cdf

public double cdf(double x)

Description copied from interface: Distribution

Returns the distribution function F(x).

Specified by:

cdf in interface Distribution

Overrides:

cdf in class HypoExponentialDist

Parameters:

x - value at which the distribution function is evaluated

Returns:

distribution function evaluated at x

barF

public double barF(double x)

Description copied from class: ContinuousDistribution

Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).

Specified by:

barF in interface Distribution

Overrides:

barF in class HypoExponentialDist

Parameters:

x - value at which the complementary distribution function is evaluated

Returns:

complementary distribution function evaluated at x

inverseF

public double inverseF(double u)

Description copied from class: ContinuousDistribution

Returns the inverse distribution function x = F^-1(u). Restrictions: u∈[0, 1].

Specified by:

inverseF in interface Distribution

Overrides:

inverseF in class HypoExponentialDist

Parameters:

u - value at which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

density

public 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.

Parameters:

n - max possible number of λ_i

k - effective number of λ_i

h - step between two successive λ_i

x - value at which the distribution is evaluated

Returns:

density at x

cdf

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

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

Parameters:

n - max possible number of λ_i

k - effective number of λ_i

h - step between two successive λ_i

x - value at which the distribution is evaluated

Returns:

value of distribution at x

barF

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

Computes the complementary distribution bar(F)(x), as in formula.

Parameters:

n - max possible number of λ_i

k - effective number of λ_i

h - step between two successive λ_i

x - value at which the complementary distribution is evaluated

Returns:

value of complementary distribution at x

inverseF

public 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.

Parameters:

n - max possible number of λ_i

k - effective number of λ_i

h - step between two successive λ_i

u - value at which the inverse distribution is evaluated

Returns:

inverse distribution at u

getParams

public double[] getParams()

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

Specified by:

getParams in interface Distribution

Overrides:

getParams in class HypoExponentialDist

Returns:

parameters of the hypoexponential distribution

setParams

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

toString

public String toString()

Overrides:

toString in class HypoExponentialDist