dists.lsp

   1 ;;;; dists -- Lisp-Stat interface to basic probability distribution routines
   2 ;;;;
   3 ;;;; Copyright (c) 1991, by Luke Tierney. Permission is granted for
   4 ;;;; unrestricted use.
   5
   6 ;;;;
   7 ;;;; Package Setup
   8 ;;;;
   9
  10 #+:CLtL2
  11 (in-package lisp-stat-basics)
  12 #-:CLtL2
  13 (in-package 'lisp-stat-basics)
  14
  15 (export '(log-gamma uniform-rand normal-cdf normal-quant normal-dens
  16           normal-rand bivnorm-cdf cauchy-cdf cauchy-quant cauchy-dens
  17           cauchy-rand gamma-cdf gamma-quant gamma-dens gamma-rand
  18           chisq-cdf chisq-quant chisq-dens chisq-rand beta-cdf beta-quant
  19           beta-dens beta-rand t-cdf t-quant t-dens t-rand f-cdf f-quant
  20           f-dens f-rand poisson-cdf poisson-quant poisson-pmf poisson-rand
  21           binomial-cdf binomial-quant binomial-pmf binomial-rand))
  22
  23 (defmacro defbaserand (name onefun &rest args)
  24   `(defun ,name (n ,@args)
  25      (let ((result nil))
  26        (dotimes (i n result)
  27                 (declare (fixnum i) (inline ,onefun))
  28                 (setf result (cons (,onefun ,@args) result))))))
  29
  30 (defbaserand base-uniform-rand one-uniform-rand)
  31 (defbaserand base-normal-rand one-normal-rand)
  32 (defbaserand base-cauchy-rand one-cauchy-rand)
  33 (defbaserand base-gamma-rand one-gamma-rand a)
  34 (defbaserand base-chisq-rand one-chisq-rand df)
  35 (defbaserand base-beta-rand one-beta-rand a b)
  36 (defbaserand base-t-rand one-t-rand df)
  37 (defbaserand base-f-rand one-f-rand ndf ddf)
  38 (defbaserand base-poisson-rand one-poisson-rand a)
  39 (defbaserand base-binomial-rand one-binomial-rand a b)
  40
  41 (make-rv-function log-gamma base-log-gamma x)
  42
  43 (make-rv-function uniform-rand base-uniform-rand n)
  44
  45 (make-rv-function normal-cdf base-normal-cdf x)
  46 (make-rv-function normal-quant base-normal-quant p)
  47 (make-rv-function normal-dens base-normal-dens x)
  48 (make-rv-function normal-rand base-normal-rand n)
  49 (make-rv-function bivnorm-cdf base-bivnorm-cdf x y r)
  50
  51 (make-rv-function cauchy-cdf base-cauchy-cdf x)
  52 (make-rv-function cauchy-quant base-cauchy-quant p)
  53 (make-rv-function cauchy-dens base-cauchy-dens x)
  54 (make-rv-function cauchy-rand base-cauchy-rand n)
  55
  56 (make-rv-function gamma-cdf base-gamma-cdf x a)
  57 (make-rv-function gamma-quant base-gamma-quant p a)
  58 (make-rv-function gamma-dens base-gamma-dens x a)
  59 (make-rv-function gamma-rand base-gamma-rand n a)
  60
  61 (make-rv-function chisq-cdf base-chisq-cdf x df)
  62 (make-rv-function chisq-quant base-chisq-quant p df)
  63 (make-rv-function chisq-dens base-chisq-dens x df)
  64 (make-rv-function chisq-rand base-chisq-rand n df)
  65
  66 (make-rv-function beta-cdf base-beta-cdf x a b)
  67 (make-rv-function beta-quant base-beta-quant p a b)
  68 (make-rv-function beta-dens base-beta-dens x a b)
  69 (make-rv-function beta-rand base-beta-rand n a b)
  70
  71 (make-rv-function t-cdf base-t-cdf x df)
  72 (make-rv-function t-quant base-t-quant p df)
  73 (make-rv-function t-dens base-t-dens x df)
  74 (make-rv-function t-rand base-t-rand n df)
  75
  76 (make-rv-function f-cdf base-f-cdf x ndf ddf)
  77 (make-rv-function f-quant base-f-quant p ndf ddf)
  78 (make-rv-function f-dens base-f-dens x ndf ddf)
  79 (make-rv-function f-rand base-f-rand n ndf ddf)
  80
  81 (make-rv-function poisson-cdf base-poisson-cdf x a)
  82 (make-rv-function poisson-quant base-poisson-quant p a)
  83 (make-rv-function poisson-pmf base-poisson-pmf x a)
  84 (make-rv-function poisson-rand base-poisson-rand n a)
  85
  86 (make-rv-function binomial-cdf base-binomial-cdf x a b)
  87 (make-rv-function binomial-quant base-binomial-quant p a b)
  88 (make-rv-function binomial-pmf base-binomial-pmf x a b)
  89 (make-rv-function binomial-rand base-binomial-rand n a b)
  90
  91 ;;;;
  92 ;;;; Documentation
  93 ;;;;
  94
  95 (setf (documentation 'bivnorm-cdf 'function)
  96 "Args: (x y r)
  97 Returns the value of the standard bivariate normal distribution function
  98 with correlation R at (X, Y). Vectorized.")
  99
 100 (setf (documentation 'normal-cdf 'function)
 101 "Args: (x)
 102 Returns the value of the standard normal distribution function at X.
 103 Vectorized.")
 104
 105 (setf (documentation 'beta-cdf 'function)
 106 "Args: (x alpha beta)
 107 Returns the value of the Beta(ALPHA, BETA) distribution function at X.
 108 Vectorized.")
 109
 110 (setf (documentation 'gamma-cdf 'function)
 111 "Args: (x alpha)
 112 Returns the value of the Gamma(alpha, 1) distribution function at X.
 113 Vectorized.")
 114
 115 (setf (documentation 'chisq-cdf 'function)
 116 "Args: (x df)
 117 Returns the value of the Chi-Square(DF) distribution function at X. Vectorized.")
 118
 119 (setf (documentation 't-cdf 'function)
 120 "Args: (x df)
 121 Returns the value of the T(DF) distribution function at X. Vectorized.")
 122
 123 (setf (documentation 'f-cdf 'function)
 124 "Args: (x ndf ddf)
 125 Returns the value of the F(NDF, DDF) distribution function at X. Vectorized.")
 126
 127 (setf (documentation 'cauchy-cdf 'function)
 128 "Args: (x)
 129 Returns the value of the standard Cauchy distribution function at X.
 130 Vectorized.")
 131
 132 (setf (documentation 'log-gamma 'function)
 133 "Args: (x)
 134 Returns the log gamma function of X. Vectorized.")
 135
 136 (setf (documentation 'normal-quant 'function)
 137 "Args (p)
 138 Returns the P-th quantile of the standard normal distribution. Vectorized.")
 139
 140 (setf (documentation 'cauchy-quant 'function)
 141 "Args (p)
 142 Returns the P-th quantile(s) of the standard Cauchy distribution. Vectorized.")
 143
 144 (setf (documentation 'beta-quant 'function)
 145 "Args: (p alpha beta)
 146 Returns the P-th quantile of the Beta(ALPHA, BETA) distribution. Vectorized.")
 147
 148 (setf (documentation 'gamma-quant 'function)
 149 "Args: (p alpha)
 150 Returns the P-th quantile of the Gamma(ALPHA, 1) distribution. Vectorized.")
 151
 152 (setf (documentation 'chisq-quant 'function)
 153 "Args: (p df)
 154 Returns the P-th quantile of the Chi-Square(DF) distribution. Vectorized.")
 155
 156 (setf (documentation 't-quant 'function)
 157 "Args: (p df)
 158 Returns the P-th quantile of the T(DF) distribution. Vectorized.")
 159
 160 (setf (documentation 'f-quant 'function)
 161 "Args: (p ndf ddf)
 162 Returns the P-th quantile of the F(NDF, DDF) distribution. Vectorized.")
 163
 164 (setf (documentation 'normal-dens 'function)
 165 "Args: (x)
 166 Returns the density at X of the standard normal distribution. Vectorized.")
 167
 168 (setf (documentation 'cauchy-dens 'function)
 169 "Args: (x)
 170 Returns the density at X of the standard Cauchy distribution. Vectorized.")
 171
 172 (setf (documentation 'beta-dens 'function)
 173 "Args: (x alpha beta)
 174 Returns the density at X of the Beta(ALPHA, BETA) distribution. Vectorized.")
 175
 176 (setf (documentation 'gamma-dens 'function)
 177 "Args: (x alpha)
 178 Returns the density at X of the Gamma(ALPHA, 1) distribution. Vectorized.")
 179
 180 (setf (documentation 'chisq-dens 'function)
 181 "Args: (x alpha)
 182 Returns the density at X of the Chi-Square(DF) distribution. Vectorized.")
 183
 184 (setf (documentation 't-dens 'function)
 185 "Args: (x alpha)
 186 Returns the density at X of the T(DF) distribution. Vectorized.")
 187
 188 (setf (documentation 'f-dens 'function)
 189 "Args: (x ndf ddf)
 190 Returns the density at X of the F(NDF, DDF) distribution. Vectorized.")
 191
 192 (setf (documentation 'uniform-rand 'function)
 193 "Args: (n)
 194 Returns a list of N uniform random variables from the range (0, 1).
 195 Vectorized.")
 196
 197 (setf (documentation 'normal-rand 'function)
 198 "Args: (n)
 199 Returns a list of N standard normal random numbers. Vectorized.")
 200
 201 (setf (documentation 'cauchy-rand 'function)
 202 "Args: (n)
 203 Returns a list of N standard Cauchy random numbers. Vectorized.")
 204
 205 (setf (documentation 't-rand 'function)
 206 "Args: (n df)
 207 Returns a list of N T(DF) random variables. Vectorized.")
 208
 209 (setf (documentation 'f-rand 'function)
 210 "Args: (n ndf ddf)
 211 Returns a list of N F(NDF, DDF) random variables. Vectorized.")
 212
 213 (setf (documentation 'gamma-rand 'function)
 214 "Args: (n a)
 215 Returns a list of N Gamma(A, 1) random variables. Vectorized.")
 216
 217 (setf (documentation 'chisq-rand 'function)
 218 "Args: (n df)
 219 Returns a list of N Chi-Square(DF) random variables. Vectorized.")
 220
 221 (setf (documentation 'beta-rand 'function)
 222 "Args: (n a b)
 223 Returns a list of N beta(A, B) random variables. Vectorized.")
 224
 225 (setf (documentation 'binomial-cdf 'function)
 226 "Args (x n p)
 227 Returns value of the Binomial(N, P) distribution function at X. Vectorized.")
 228
 229 (setf (documentation 'poisson-cdf 'function)
 230 "Args (x mu)
 231 Returns value of the Poisson(MU) distribution function at X. Vectorized.")
 232
 233 (setf (documentation 'binomial-pmf 'function)
 234 "Args (k n p)
 235 Returns value of the Binomial(N, P) pmf function at integer K. Vectorized.")
 236
 237 (setf (documentation 'poisson-pmf 'function)
 238 "Args (k mu)
 239 Returns value of the Poisson(MU) pmf function at integer K. Vectorized.")
 240
 241 (setf (documentation 'binomial-quant 'function)
 242 "Args: (x n p)
 243 Returns x-th quantile (left continuous inverse) of Binomial(N, P) cdf.
 244 Vectorized.")
 245
 246 (setf (documentation 'poisson-quant 'function)
 247 "Args: (x mu)
 248 Returns x-th quantile (left continuous inverse) of Poisson(MU) cdf.
 249 Vectorized.")
 250
 251 (setf (documentation 'binomial-rand 'function)
 252 "Args: (k n p)
 253 Returns list of K draws from the Binomial(N, P) distribution. Vectorized.")
 254
 255 (setf (documentation 'poisson-rand 'function)
 256 "Args: (k mu)
 257 Returns list of K draws from the Poisson(MU) distribution. Vectorized.")