Provides a variant of ChiSquareDist with faster but less accurate methods. More...
Public Member Functions | |
| ChiSquareDistQuick (int n) | |
Constructs a chi-square distribution with n degrees of freedom. | |
| double | inverseF (double u) |
| Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More... | |
 Public Member Functions inherited from ChiSquareDist | |
| ChiSquareDist (int n) | |
Constructs a chi-square distribution with n degrees of freedom. | |
| 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. | |
| int | getN () |
| Returns the parameter \(n\) of this object. | |
| void | setN (int n) |
| Sets the parameter \(n\) of this object. | |
| double [] | getParams () |
| Return a table containing the parameters of the current distribution. | |
| 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 | inverseF (int n, double u) |
| Computes a quick-and-dirty approximation of \(F^{-1}(u)\), where \(F\) is the chi-square distribution with \(n\) degrees of freedom. More... | |
| Static Public Member Functions inherited from ChiSquareDist | |
| static double | density (int n, double x) |
| Computes the density function ( Fchi2 ) for a chi-square distribution with \(n\) degrees of freedom. | |
| static double | cdf (int n, int d, double x) |
| Computes the chi-square distribution function with \(n\) degrees of freedom, evaluated at \(x\). More... | |
| static double | barF (int n, int d, double x) |
| Computes the complementary chi-square distribution function with \(n\) degrees of freedom, evaluated at \(x\). More... | |
| static double | inverseF (int n, double u) |
| Computes an approximation of \(F^{-1}(u)\), where \(F\) is the chi-square distribution with \(n\) degrees of freedom. More... | |
| static double [] | getMLE (double[] x, int m) |
| Estimates the parameter \(n\) of the chi-square distribution using the maximum likelihood method, from the \(m\) observations \(x[i]\), \(i = 0, 1, …, m-1\). More... | |
| static ChiSquareDist | getInstanceFromMLE (double[] x, int m) |
| Creates a new instance of a chi-square distribution with parameter \(n\) estimated using the maximum likelihood method based on the \(m\) observations \(x[i]\), \(i = 0, 1, …, m-1\). More... | |
| static double | getMean (int n) |
| Computes and returns the mean \(E[X] = n\) of the chi-square distribution with parameter \(n\). More... | |
| static double [] | getMomentsEstimate (double[] x, int m) |
| Estimates and returns the parameter [ \(\hat{n}\)] of the chi-square distribution using the moments method based on the \(m\) observations in table \(x[i]\), \(i = 0, 1, …, m-1\). More... | |
| static double | getVariance (int n) |
| Returns the variance \(\mbox{Var}[X] = 2n\) of the chi-square distribution with parameter \(n\). More... | |
| static double | getStandardDeviation (int n) |
| Returns the standard deviation of the chi-square distribution with parameter \(n\). More... | |
Additional Inherited Members | |
| Public Attributes inherited from ContinuousDistribution | |
| int | decPrec = 15 |
| Protected Attributes inherited from ChiSquareDist | |
| int | n |
| double | C1 |
| 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
Provides a variant of ChiSquareDist with faster but less accurate methods.
The non-static version of inverseF calls the static version. This method is not very accurate for small \(n\) but becomes better as \(n\) increases. The other methods are the same as in ChiSquareDist.
Member Function Documentation
◆ 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 |
Computes a quick-and-dirty approximation of \(F^{-1}(u)\), where \(F\) is the chi-square distribution with \(n\) degrees of freedom.
Uses the approximation given in Figure L.24 of [25] over most of the range. For \(u < 0.02\) or \(u > 0.98\), it uses the approximation given in [73] for \(n \ge10\), and returns 2.0 * inverseF(n/2, 6, u) for \(n < 10\) in order to avoid the loss of precision of the above approximations. When \(n \ge10\) or \(0.02 < u < 0.98\), it is between 20 to 30 times faster than the same method in ChiSquareDist for \(n\) between \(10\) and \(1000\) and even faster for larger \(n\).
Note that the number \(d\) of decimal digits of precision generally increases with \(n\). For \(n=3\), we only have \(d = 3\) over most of the range. For \(n=10\), \(d=5\) except far in the tails where \(d = 3\). For \(n=100\), one has more than \(d=7\) over most of the range and for \(n=1000\), at least \(d=8\). The cases \(n = 1\) and \(n = 2\) are exceptions, with precision of about \(d=10\).
The documentation for this class was generated from the following file:
- ChiSquareDistQuick.java
