## Contents (2008)

### BibTeX

@MISC{Classes08contents,

author = {General Classes},

title = {Contents},

year = {2008}

}

### OpenURL

### Abstract

This package provides tools to compute densities, mass functions, distribution functions

### Citations

1333 | Simulation Modeling and Analysis - Law, Kelton - 1991 |

283 |
A Guide to Simulation
- Bratley, Fox, et al.
- 1983
(Show Context)
Citation Context ...ic 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. Uses the approximation given in [1] and in Figure L.23 of =-=[6]-=-. It gives at leastMay 21, 2008 ChiSquareDist 38 6 decimal digits of precision, except far in the tails (that is, for u < 10 −5 or u > 1 − 10 −5 ) where the function calls the method GammaDist.invers... |

118 | Random number generation and Monte Carlo methods - Gentle |

68 | Approximating Integrals Via Monte Carlo and Deterministic Methods - Evans, Swartz - 2000 |

44 | Statistical Computing - Kennedy, Gentle - 1981 |

25 |
Computer generation of hypergeometric random variates
- Kachitvichyanukul, Schmeiser
- 1985
(Show Context)
Citation Context ...lic static int inverseF (int m, int l, int k, double u) Computes F −1 (u) for the hypergeometric distribution without using precomputed tables. The inversion is computed using the chop-down algorithm =-=[17]-=-. public static double getMean (int m, int l, int k) Computes and returns the mean E[X] = km/l of the Hypergeometric distribution with parameters m, l and k. public static double getVariance (int m, i... |

22 |
A new family of life distributions
- Birnbaum, Saunders
- 1969
(Show Context)
Citation Context ...lic void setParams (double alpha, double lambda) Sets the parameters α and λ of this object.May 21, 2008 46 FatigueLifeDist Extends the class ContinuousDistribution for the Fatigue Life distribution =-=[3]-=- with location parameter µ, scale parameter β and shape parameter γ. Its density is ⎡√ x−µ ⎢ β f(x) = ⎣ + √ ⎤ ⎛√ β x−µ x−µ ⎥ ⎜ β ⎦ φ ⎝ 2γ(x − µ) − √ ⎞ β x−µ ⎟ ⎠ , for x > µ, (36) γ where φ is the prob... |

15 |
UNURAN—A Library for Universal Non-Uniform Random Number Generators, 2002. Available at http://statistik.wu-wien.ac.at/unuran
- Leydold, Hörmann
(Show Context)
Citation Context ...ibution objects from a string. This permits one to obtain distribution specifications from a file or dynamically from user input during program execution. This string API is similar to that of UNURAN =-=[20]-=-. The (static) methods of this class invoke the constructor specified in the string. For example, d = DistributionFactory.getContinuousDistribution ("NormalDist (0.0, 2.5)"); is equivalent to d = Norm... |

11 |
Zaman: Rapid evaluation of the inverse of the normal distribution function
- Marsaglia, Marsaglia, et al.
- 1994
(Show Context)
Citation Context ...public static double cdf (double mu, double sigma, double x) Returns an approximation of Φ(x), where Φ is the standard normal distribution function, with mean 0 and variance 1. Uses Marsaglia et al’s =-=[22]-=- fast method with table lookups. Returns 15 decimal digits of precision. This method is approximately 60% faster than NormalDist.cdf. public static double barF01 (double x) Same as barF (0.0, 1.0, x).... |

10 |
Rational Chebyshev approximations for the inverse of the error function
- Blair, Edwards, et al.
- 1976
(Show Context)
Citation Context ... mu, double sigma, double u) Computes the inverse normal distribution function with mean µ and variance σ2 . Uses rational Chebyshev approximations giving at least 16 decimal digits of precision (see =-=[4]-=-). public static NormalDist getInstanceFromMLE (double[] x, int n) Creates a new instance of a normal distribution with parameters µ and σ estimated using the maximum likelihood method based on the n ... |

10 | Simple Approximation to the Poisson, Binomial and Hypergeometric Distribution - Molenaar - 1971 |

8 |
Algorithm 395: Students t-distribution
- Hill
- 1970
(Show Context)
Citation Context ...udent-t distribution function with n degrees of freedom. Uses an approximation giving at least 5 decimal digits of precision when n ≥ 8 or n ≤ 2, and 3 decimal digits of precision when 3 ≤ n ≤ 7 (see =-=[13]-=- and Figure L.28 of [6]). public static StudentDist getInstanceFromMLE (double[] x, int m) Creates a new instance of a Student-t distribution with parameter n estimated using the maximum likelihood me... |

8 |
A normal approximation for binomial, F, Beta, and other common, related tail probabilities II
- Pratt
- 1968
(Show Context)
Citation Context ...e to 0 and α > 1, x close to 1/2 and α < 1, and x close to 1/2 and α > 1), which are then solved by Newton’s method for the solution of equations. For α > 100000, uses a normal approximation given in =-=[25]-=-.May 21, 2008 BetaSymmetricalDist 32 public static BetaDist getInstanceFromMLE (double[] x, int n) Creates a new instance of a symmetrical beta distribution with parameter α estimated using the maxim... |

8 | UNCMIN—Unconstrained Optimization Package, FORTRAN - Schnabel |

8 |
Chebyshev expansions for the error and related functions
- SCHONFELDER
- 1978
(Show Context)
Citation Context ...s cdf (0.0, 1.0, x). public static double cdf (double mu, double sigma, double x) Computes the normal distribution function with mean µ and variance σ 2 . Uses the Chebyshev approximation proposed in =-=[27]-=-, which gives 16 decimals of precision. public static double barF01 (double x) Same as barF (0.0, 1.0, x).May 21, 2008 NormalDist 69 public static double barF (double mu, double sigma, double x) Comp... |

7 | Tables of the F and Related Distributions with Algorithms - Mardia, Zemroch - 1978 |

5 | 1951]: "Approximation to the point binomial - Camp - 1951 |

5 | Certification of algorithm 222: Incomplete beta function ratios - Gautschi - 1964 |

5 |
Cephes math library
- Moshier
- 2000
(Show Context)
Citation Context ...ha, beta, 0, 1, d, u). public static double inverseF (double alpha, double beta, double a, double b, int d, double u) Returns the inverse beta distribution function using the algorithm implemented in =-=[24]-=-. The method performs interval halving or Newton iterations to compute the inverse. The precision depends on the accuracy of the cdf method. The argument d gives a good idea of the precision attained.... |

4 |
Algorithm AS 91: The percentage points of the χ 2 distribution
- Best, Roberts
- 1975
(Show Context)
Citation Context ...are assumed to be sorted by increasing order. Methods public double prob (int k) Returns pk, the probability of the k-th observation, for 0 ≤ k < n. The result should be a real number in the interval =-=[0, 1]-=-. public double getMean() Computes the mean E[X] = ∑ n i=1 pixi of the distribution. public double getVariance() Computes the variance Var[X] = ∑ n i=1 pi(xi − E[X]) 2 of the distribution. public doub... |

4 |
The incomplete gamma integral
- Bhattacharjee
- 1970
(Show Context)
Citation Context ...e x) Returns an approximation of the gamma distribution function with parameters α = alpha and λ = lambda, whose density is given by (39). The approximation is an improved version of the algorithm in =-=[2]-=-. The function tries to return d decimals digits of precision. For α not too large (e.g., α ≤ 1000), d gives a good idea of the precision attained. public static double cdf (double alpha, int d, doubl... |

4 | Some applications of Pearson transformations - Bol’shev - 1964 |

4 |
Algorithm 451: Chi-square quantiles
- Goldstein
- 1973
(Show Context)
Citation Context ...ere F is the chi-square distribution with n degrees of freedom. Uses the approximation given in Figure L.24 of [6] over most of the range. For u < 0.02 or u > 0.98, it uses the approximation given in =-=[12]-=- for n ≥ 10, and returns 2.0 * GammaDist.inverseF (n/2, 6, u) for n < 10 in order to avoid the loss of precision of the above approximations. When n ≥ 10 or 0.02 < u < 0.98, it is between 20 to 30 tim... |

4 | UNCMIN—Unconstrained Optimization Package - Verrill |