dists.lsp

   1 ;;; -*- mode: lisp -*-
   2 ;;; Copyright (c) 2005--2007, by A.J. Rossini <blindglobe@gmail.com>
   3 ;;; See COPYRIGHT file for any additional restrictions (BSD license).
   4 ;;; Since 1991, ANSI was finally finished.  Edited for ANSI Common Lisp.
   5
   6 ;;;; dists -- Lisp-Stat interface to basic probability distribution routines
   7 ;;;;
   8 ;;;; Copyright (c) 1991, by Luke Tierney. Permission is granted for
   9 ;;;; unrestricted use.
  10
  11 ;;;;
  12 ;;;; Package Setup
  13 ;;;;
  14
  15
  16 (in-package :lisp-stat-basics)
  17
  18 (export '(log-gamma uniform-rand normal-cdf normal-quant normal-dens
  19           normal-rand bivnorm-cdf cauchy-cdf cauchy-quant cauchy-dens
  20           cauchy-rand gamma-cdf gamma-quant gamma-dens gamma-rand
  21           chisq-cdf chisq-quant chisq-dens chisq-rand beta-cdf beta-quant
  22           beta-dens beta-rand t-cdf t-quant t-dens t-rand f-cdf f-quant
  23           f-dens f-rand poisson-cdf poisson-quant poisson-pmf poisson-rand
  24           binomial-cdf binomial-quant binomial-pmf binomial-rand))
  25
  26 (defmacro defbaserand (name onefun &rest args)
  27   `(defun ,name (n ,@args)
  28      (let ((result nil))
  29        (dotimes (i n result)
  30                 (declare (fixnum i) (inline ,onefun))
  31                 (setf result (cons (,onefun ,@args) result))))))
  32
  33 (defbaserand base-uniform-rand one-uniform-rand)
  34 (defbaserand base-normal-rand one-normal-rand)
  35 (defbaserand base-cauchy-rand one-cauchy-rand)
  36 (defbaserand base-gamma-rand one-gamma-rand a)
  37 (defbaserand base-chisq-rand one-chisq-rand df)
  38 (defbaserand base-beta-rand one-beta-rand a b)
  39 (defbaserand base-t-rand one-t-rand df)
  40 (defbaserand base-f-rand one-f-rand ndf ddf)
  41 (defbaserand base-poisson-rand one-poisson-rand a)
  42 (defbaserand base-binomial-rand one-binomial-rand a b)
  43
  44 (make-rv-function log-gamma base-log-gamma x)
  45
  46 (make-rv-function uniform-rand base-uniform-rand n)
  47
  48 (make-rv-function normal-cdf base-normal-cdf x)
  49 (make-rv-function normal-quant base-normal-quant p)
  50 (make-rv-function normal-dens base-normal-dens x)
  51 (make-rv-function normal-rand base-normal-rand n)
  52 (make-rv-function bivnorm-cdf base-bivnorm-cdf x y r)
  53
  54 (make-rv-function cauchy-cdf base-cauchy-cdf x)
  55 (make-rv-function cauchy-quant base-cauchy-quant p)
  56 (make-rv-function cauchy-dens base-cauchy-dens x)
  57 (make-rv-function cauchy-rand base-cauchy-rand n)
  58
  59 (make-rv-function gamma-cdf base-gamma-cdf x a)
  60 (make-rv-function gamma-quant base-gamma-quant p a)
  61 (make-rv-function gamma-dens base-gamma-dens x a)
  62 (make-rv-function gamma-rand base-gamma-rand n a)
  63
  64 (make-rv-function chisq-cdf base-chisq-cdf x df)
  65 (make-rv-function chisq-quant base-chisq-quant p df)
  66 (make-rv-function chisq-dens base-chisq-dens x df)
  67 (make-rv-function chisq-rand base-chisq-rand n df)
  68
  69 (make-rv-function beta-cdf base-beta-cdf x a b)
  70 (make-rv-function beta-quant base-beta-quant p a b)
  71 (make-rv-function beta-dens base-beta-dens x a b)
  72 (make-rv-function beta-rand base-beta-rand n a b)
  73
  74 (make-rv-function t-cdf base-t-cdf x df)
  75 (make-rv-function t-quant base-t-quant p df)
  76 (make-rv-function t-dens base-t-dens x df)
  77 (make-rv-function t-rand base-t-rand n df)
  78
  79 (make-rv-function f-cdf base-f-cdf x ndf ddf)
  80 (make-rv-function f-quant base-f-quant p ndf ddf)
  81 (make-rv-function f-dens base-f-dens x ndf ddf)
  82 (make-rv-function f-rand base-f-rand n ndf ddf)
  83
  84 (make-rv-function poisson-cdf base-poisson-cdf x a)
  85 (make-rv-function poisson-quant base-poisson-quant p a)
  86 (make-rv-function poisson-pmf base-poisson-pmf x a)
  87 (make-rv-function poisson-rand base-poisson-rand n a)
  88
  89 (make-rv-function binomial-cdf base-binomial-cdf x a b)
  90 (make-rv-function binomial-quant base-binomial-quant p a b)
  91 (make-rv-function binomial-pmf base-binomial-pmf x a b)
  92 (make-rv-function binomial-rand base-binomial-rand n a b)
  93
  94 ;;;;
  95 ;;;; Documentation
  96 ;;;;
  97
  98 (setf (documentation 'bivnorm-cdf 'function)
  99 "Args: (x y r)
 100 Returns the value of the standard bivariate normal distribution function
 101 with correlation R at (X, Y). Vectorized.")
 102
 103 (setf (documentation 'normal-cdf 'function)
 104 "Args: (x)
 105 Returns the value of the standard normal distribution function at X.
 106 Vectorized.")
 107
 108 (setf (documentation 'beta-cdf 'function)
 109 "Args: (x alpha beta)
 110 Returns the value of the Beta(ALPHA, BETA) distribution function at X.
 111 Vectorized.")
 112
 113 (setf (documentation 'gamma-cdf 'function)
 114 "Args: (x alpha)
 115 Returns the value of the Gamma(alpha, 1) distribution function at X.
 116 Vectorized.")
 117
 118 (setf (documentation 'chisq-cdf 'function)
 119 "Args: (x df)
 120 Returns the value of the Chi-Square(DF) distribution function at X. Vectorized.")
 121
 122 (setf (documentation 't-cdf 'function)
 123 "Args: (x df)
 124 Returns the value of the T(DF) distribution function at X. Vectorized.")
 125
 126 (setf (documentation 'f-cdf 'function)
 127 "Args: (x ndf ddf)
 128 Returns the value of the F(NDF, DDF) distribution function at X. Vectorized.")
 129
 130 (setf (documentation 'cauchy-cdf 'function)
 131 "Args: (x)
 132 Returns the value of the standard Cauchy distribution function at X.
 133 Vectorized.")
 134
 135 (setf (documentation 'log-gamma 'function)
 136 "Args: (x)
 137 Returns the log gamma function of X. Vectorized.")
 138
 139 (setf (documentation 'normal-quant 'function)
 140 "Args (p)
 141 Returns the P-th quantile of the standard normal distribution. Vectorized.")
 142
 143 (setf (documentation 'cauchy-quant 'function)
 144 "Args (p)
 145 Returns the P-th quantile(s) of the standard Cauchy distribution. Vectorized.")
 146
 147 (setf (documentation 'beta-quant 'function)
 148 "Args: (p alpha beta)
 149 Returns the P-th quantile of the Beta(ALPHA, BETA) distribution. Vectorized.")
 150
 151 (setf (documentation 'gamma-quant 'function)
 152 "Args: (p alpha)
 153 Returns the P-th quantile of the Gamma(ALPHA, 1) distribution. Vectorized.")
 154
 155 (setf (documentation 'chisq-quant 'function)
 156 "Args: (p df)
 157 Returns the P-th quantile of the Chi-Square(DF) distribution. Vectorized.")
 158
 159 (setf (documentation 't-quant 'function)
 160 "Args: (p df)
 161 Returns the P-th quantile of the T(DF) distribution. Vectorized.")
 162
 163 (setf (documentation 'f-quant 'function)
 164 "Args: (p ndf ddf)
 165 Returns the P-th quantile of the F(NDF, DDF) distribution. Vectorized.")
 166
 167 (setf (documentation 'normal-dens 'function)
 168 "Args: (x)
 169 Returns the density at X of the standard normal distribution. Vectorized.")
 170
 171 (setf (documentation 'cauchy-dens 'function)
 172 "Args: (x)
 173 Returns the density at X of the standard Cauchy distribution. Vectorized.")
 174
 175 (setf (documentation 'beta-dens 'function)
 176 "Args: (x alpha beta)
 177 Returns the density at X of the Beta(ALPHA, BETA) distribution. Vectorized.")
 178
 179 (setf (documentation 'gamma-dens 'function)
 180 "Args: (x alpha)
 181 Returns the density at X of the Gamma(ALPHA, 1) distribution. Vectorized.")
 182
 183 (setf (documentation 'chisq-dens 'function)
 184 "Args: (x alpha)
 185 Returns the density at X of the Chi-Square(DF) distribution. Vectorized.")
 186
 187 (setf (documentation 't-dens 'function)
 188 "Args: (x alpha)
 189 Returns the density at X of the T(DF) distribution. Vectorized.")
 190
 191 (setf (documentation 'f-dens 'function)
 192 "Args: (x ndf ddf)
 193 Returns the density at X of the F(NDF, DDF) distribution. Vectorized.")
 194
 195 (setf (documentation 'uniform-rand 'function)
 196 "Args: (n)
 197 Returns a list of N uniform random variables from the range (0, 1).
 198 Vectorized.")
 199
 200 (setf (documentation 'normal-rand 'function)
 201 "Args: (n)
 202 Returns a list of N standard normal random numbers. Vectorized.")
 203
 204 (setf (documentation 'cauchy-rand 'function)
 205 "Args: (n)
 206 Returns a list of N standard Cauchy random numbers. Vectorized.")
 207
 208 (setf (documentation 't-rand 'function)
 209 "Args: (n df)
 210 Returns a list of N T(DF) random variables. Vectorized.")
 211
 212 (setf (documentation 'f-rand 'function)
 213 "Args: (n ndf ddf)
 214 Returns a list of N F(NDF, DDF) random variables. Vectorized.")
 215
 216 (setf (documentation 'gamma-rand 'function)
 217 "Args: (n a)
 218 Returns a list of N Gamma(A, 1) random variables. Vectorized.")
 219
 220 (setf (documentation 'chisq-rand 'function)
 221 "Args: (n df)
 222 Returns a list of N Chi-Square(DF) random variables. Vectorized.")
 223
 224 (setf (documentation 'beta-rand 'function)
 225 "Args: (n a b)
 226 Returns a list of N beta(A, B) random variables. Vectorized.")
 227
 228 (setf (documentation 'binomial-cdf 'function)
 229 "Args (x n p)
 230 Returns value of the Binomial(N, P) distribution function at X. Vectorized.")
 231
 232 (setf (documentation 'poisson-cdf 'function)
 233 "Args (x mu)
 234 Returns value of the Poisson(MU) distribution function at X. Vectorized.")
 235
 236 (setf (documentation 'binomial-pmf 'function)
 237 "Args (k n p)
 238 Returns value of the Binomial(N, P) pmf function at integer K. Vectorized.")
 239
 240 (setf (documentation 'poisson-pmf 'function)
 241 "Args (k mu)
 242 Returns value of the Poisson(MU) pmf function at integer K. Vectorized.")
 243
 244 (setf (documentation 'binomial-quant 'function)
 245 "Args: (x n p)
 246 Returns x-th quantile (left continuous inverse) of Binomial(N, P) cdf.
 247 Vectorized.")
 248
 249 (setf (documentation 'poisson-quant 'function)
 250 "Args: (x mu)
 251 Returns x-th quantile (left continuous inverse) of Poisson(MU) cdf.
 252 Vectorized.")
 253
 254 (setf (documentation 'binomial-rand 'function)
 255 "Args: (k n p)
 256 Returns list of K draws from the Binomial(N, P) distribution. Vectorized.")
 257
 258 (setf (documentation 'poisson-rand 'function)
 259 "Args: (k mu)
 260 Returns list of K draws from the Poisson(MU) distribution. Vectorized.")