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randgen.h
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222 lines (176 loc) · 12.6 KB
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/**
These are C++ classes which can be used to evaluate the probability
density functions (pdf's), cumulative distribution functions (cdf's), and
inverse distribution functions (idf's) for a variety of discrete and
continuous random variables.
The following notational conventions are used -
x : possible value of the random variable
u : real variable (probability) between 0 and 1
a, b, n, p, m, s : distribution specific parameters
There are pdf's, cdf's and idf's for 6 discrete random variables:
Random Variable Range (x) Mean Variance
Bernoulli(p) 0..1 p p*(1-p)
Binomial(n, p) 0..n n*p n*p*(1-p)
Equilikely(a, b) a..b (a+b)/2 ((b-a+1)*(b-a+1)-1)/12
Geometric(p) 0... p/(1-p) p/((1-p)*(1-p))
Pascal(n, p) 0... n*p/(1-p) n*p/((1-p)*(1-p))
Poisson(m) 0... m m
and for 8 continuous random variables:
Random Variable Range (x) Mean Variance
Uniform(a, b) a < x < b (a+b)/2 (b-a)*(b-a)/12
Exponential(m) x > 0 m m*m
Erlang(n, b) x > 0 n*b n*b*b
Normal all x 0 1
Gauss(m, s) all x m s*s
Lognormal(a, b) x > 0 see below
Chisquare(n) x > 0 n 2*n
Student(n) all x 0 (n > 1) n/(n-2) (n > 2)
For the Lognormal(a, b), the mean and variance are:
mean = Exp(a + 0.5*b*b)
variance = (Exp(b*b) - 1)*Exp(2*a + b*b)
Name : DFU.C
Purpose : Distribution/Density Function Routines
Author : Steve Park
Language : Turbo Pascal, 5.0
Latest Revision : 09-19-90
Reference : Lecture Notes on Simulation, by Steve Park
Converted to C : David W. Geyer 09-02-91
*/
/* NOTE - must link with sfu.o */
class DiscreteRV {
static double Bernoulli_pdf(double p, long x);
static double Bernoulli_cdf(double p, long x);
static long Bernoulli_idf(double p, double u);
static double Equilikely_pdf(long a, long b, long x);
static double Equilikely_cdf(long a, long b, long x);
static double Equilikely_idf(long a, long b, double u);
static double Binomial_pdf(long n, double p, long x);
static double Binomial_cdf(long n, double p, long x);
static double Binomial_idf(long n, double p, double u);
static double Geometric_pdf(double p, long x);
static double Geometric_cdf(double p, long x);
static long Geometric_idf(double p, double u);
static double Pascal_pdf(long n, double p, long x);
static double Pascal_cdf(long n, double p, long x);
static long Pascal_idf(long n, double p, double u);
static double Poisson_pdf(double m, long x);
static double Poisson_cdf(double m, long x);
static long Poisson_idf(double m, double u);
};
class ContinuousRV {
static double Uniform_pdf(double a, double b, double x);
static double Uniform_cdf(double a, double b, double x);
static double Uniform_idf(double a, double b, double u);
static double Exponential_pdf(double m, double x);
static double Exponential_cdf(double m, double x);
static double Exponential_idf(double m, double u);
static double Erlang_pdf(long n, double b, double x);
static double Erlang_cdf(long n, double b, double x);
static double Erlang_idf(long n, double b, double u);
static double Normal_pdf (double x);
static double Normal_cdf (double x);
static double Normal_idf (double u);
static double Gauss_pdf(double m, double s, double x);
static double Gauss_cdf(double m, double s, double x);
static double Gauss_idf(double m, double s, double u);
static double Lognormal_pdf(double a, double b, double x);
static double Lognormal_cdf(double a, double b, double x);
static double Lognormal_idf(double a, double b, double u);
static double Chisquare_pdf(long n, double x);
static double Chisquare_cdf(long n, double x);
static double Chisquare_idf(long n, double u);
static double Student_pdf(long n, double x);
static double Student_cdf(long n, double x);
static double Student_idf(long n, double u);
};
/* ========================================================================= */
/* double Equilikely_pdf() */
/* double Equilikely_cdf() */
/* long Equilikely_idf() */
/* */
/* NOTE: use a <= x <= b and 0 < u < 1 */
/* ========================================================================= */
/* ========================================================================= */
/* double Binomial_pdf() */
/* double Binomial_cdf() */
/* long Binomial_idf() */
/* */
/* NOTE: use 0 <= x <= n, 0 < p < 1 and 0 < u < 1 */
/* ========================================================================= */
/* ========================================================================= */
/* double Geometric_pdf() */
/* double Geometric_cdf() */
/* long Geometric_idf() */
/* */
/* NOTE: use 0 < p < 1, x >= 0 and 0 < u < 1 */
/* ========================================================================= */
/* ========================================================================= */
/* double Pascal_pdf() */
/* double Pascal_cdf() */
/* long Pascal_idf() */
/* */
/* NOTE: use n >= 1, 0 < p < 1, x >= 0 and 0 < u < 1 */
/* ========================================================================= */
/* ========================================================================= */
/* double Poisson_pdf() */
/* double Poisson_cdf() */
/* long Poisson_idf() */
/* */
/* NOTE: use m > 0, x >= 0 and 0 < u < 1 */
/* ========================================================================= */
/* ========================================================================= */
/* double Uniform_pdf() */
/* double Uniform_cdf() */
/* double Uniform_idf() */
/* */
/* NOTE: use a < x < b and 0 < u < 1 */
/* ========================================================================= */
/* ========================================================================= */
/* double Exponential_pdf() */
/* double Exponential_cdf() */
/* double Exponential_idf() */
/* */
/* NOTE: use m > 0, x > 0 and 0 < u < 1 */
/* ========================================================================= */
/* ========================================================================= */
/* double Erlang_pdf() */
/* double Erlang_cdf() */
/* double Erlang_idf() */
/* */
/* NOTE: use n >= 1, b > 0, x > 0 and 0 < u < 1 */
/* ========================================================================= */
/* ========================================================================= */
/* double Normal_pdf() */
/* double Normal_cdf() */
/* double Normal_idf() */
/* */
/* NOTE: x can be any value, but 0 < u < 1 */
/* ========================================================================= */
/* ========================================================================= */
/* double Gauss_pdf() */
/* double Gauss_cdf() */
/* double Gauss_idf() */
/* */
/* NOTE: x and m can be any value, but s > 0 and 0 < u < 1 */
/* ========================================================================= */
/* ========================================================================= */
/* double Lognormal_pdf() */
/* double Lognormal_cdf() */
/* double Lognormal_idf() */
/* */
/* NOTE: a can have any value, but b > 0, x > 0 and 0 < u < 1 */
/* ========================================================================= */
/* ========================================================================= */
/* double Chisquare_pdf() */
/* double Chisquare_cdf() */
/* double Chisquare_idf() */
/* */
/* NOTE: use n >= 1, x > 0 and 0 < u < 1 */
/* ========================================================================= */
/* ========================================================================= */
/* double Student_pdf() */
/* double Student_cdf() */
/* double Student_idf() */
/* */
/* NOTE: use n >= 1, x > 0 and 0 < u < 1 */
/* ========================================================================= */