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|
-- stats-tests.dx
import stats
-- LogSpace Float
rp = [0.1, 0.3, 0.2, 0.1]
nnp = map f_to_ls rp
(ls_to_f $ sum nnp) ~~ sum rp
> True
(ls_to_f $ ls_sum nnp) ~~ sum rp
> True
(ls_to_f $ prod nnp) ~~ prod rp
> True
ls_to_f (f_to_ls 0.0) ~~ 0.0
> True
ls_to_f (f_to_ls 0.5) ~~ 0.5
> True
ls_to_f (f_to_ls 1.0) ~~ 1.0
> True
ls_to_f (f_to_ls 2.0) ~~ 2.0
> True
ls_to_f (f_to_ls 0.1 + f_to_ls 0.2) ~~ 0.3
> True
ls_to_f (f_to_ls 0.4 * f_to_ls 0.5) ~~ 0.2
> True
ls_to_f (divide (f_to_ls 0.4) (f_to_ls 0.5)) ~~ 0.8
> True
-- Log-sum-exp
Exp (-infinity) + Exp (-infinity)
> LogSpace(-inf)
Exp infinity + Exp infinity
> LogSpace(inf)
ls_sum [Exp (-infinity), Exp (-infinity)]
> LogSpace(-inf)
ls_sum [Exp (infinity), Exp (infinity)]
> LogSpace(inf)
Exp infinity + Exp (nan)
> LogSpace(nan)
ls_sum [Exp (-infinity), Exp nan]
> LogSpace(nan)
ln $ Exp nan
> nan
is_infinite infinity
> True
is_infinite (-infinity)
> True
is_infinite 0.0
> False
is_infinite nan
> False
-- mainly cross-checking against results from R
-- bernoulli
ln (density (Bernoulli 0.6) True) ~~ -0.5108256
> True
ln (cumulative (Bernoulli 0.6) False) ~~ log 0.4
> True
ls_to_f (cumulative (Bernoulli 0.6) False) ~~ 0.4
> True
ln (survivor (Bernoulli 0.6) False) ~~ log 0.6
> True
quantile (Bernoulli 0.6) 0.39 == False
> True
quantile (Bernoulli 0.6) 0.41 == True
> True
rand_vec 5 (\k. draw (Bernoulli 0.6) k) (new_key 0) :: Fin 5=>Bool
> [False, True, True, True, True]
-- binomial
ln (density (Binomial 10 0.4) 8) ~~ -4.545315
> True
ls_to_f (density (Binomial 10 0) 0) ~~ 1.0
> True
ls_to_f (density (Binomial 10 0) 1) ~~ 0.0
> True
ls_to_f (density (Binomial 10 1) 10) ~~ 1.0
> True
ls_to_f (density (Binomial 10 1) 9) ~~ 0.0
> True
ln (cumulative (Binomial 10 0.4) 7) ~~ -0.01237076
> True
ln (survivor (Binomial 10 0.4) 7) ~~ -4.398599
> True
quantile (Binomial 10 0.4) 0.5 == 4
> True
rand_vec 5 (\k. draw (Binomial 10 0.4) k) (new_key 0) :: Fin 5=>Nat
> [1, 0, 7, 6, 7]
-- exponential
ln (density (Exponential 2.0) 3.0) ~~ -5.306853
> True
ls_to_f (density (Exponential 0) 0.0) ~~ 0.0
> True
ls_to_f (density (Exponential 0) 1.0) ~~ 0.0
> True
ln (cumulative (Exponential 2.0) 3.0) ~~ -0.002481829
> True
ln (survivor (Exponential 2.0) 3.0) ~~ -6.0
> True
quantile (Exponential 2.0) 0.5 ~~ 0.3465736
> True
rand_vec 5 (\k. draw (Exponential 2.0) k) (new_key 0) :: Fin 5=>Float
> [1.021143, 0.1418202, 0.09321166, 0.2130168, 0.4305491]
-- geometric
ln (density (Geometric 0.1) 10) ~~ -3.25083
> True
ls_to_f (density (Geometric 0.0) 1) ~~ 0.0
> True
ls_to_f (density (Geometric 0.0) 2) ~~ 0.0
> True
ls_to_f (density (Geometric 1.0) 1) ~~ 1.0
> True
ls_to_f (density (Geometric 1.0) 2) ~~ 0.0
> True
ln (cumulative (Geometric 0.1) 10) ~~ -0.4287518
> True
ln (survivor (Geometric 0.1) 10) ~~ -1.053605
> True
quantile (Geometric 0.1) 0.5 == 7
> True
ln (density (Geometric 0) 1) == -infinity
> True
ln (density (Geometric 0) 2) == -infinity
> True
ln (density (Geometric 1) 1) ~~ 0.0
> True
ln (density (Geometric 1) 2) == -infinity
> True
rand_vec 5 (\k. draw (Geometric 0.1) k) (new_key 0) :: Fin 5=>Nat
> [20, 3, 2, 5, 9]
-- normal
ln (density (Normal 1.0 2.0) 3.0) ~~ -2.112086
> True
rand_vec 5 (\k. draw (Normal 1.0 2.0) k) (new_key 0) :: Fin 5=>Float
> [-1.93355, 4.198111, 0.5292515, 0.01886255, 2.921813]
ln (cumulative (Normal 1.0 2.0) 0.5) ~~ -0.9130617
> True
ln (survivor (Normal 1.0 2.0) 0.1) ~~ -0.3950523
> True
-- poisson
ln (density (Poisson 5.0) 8) ~~ -2.7291
> True
ls_to_f (density (Poisson 0.0) 0) ~~ 1.0
> True
ls_to_f (density (Poisson 0.0) 1) ~~ 0.0
> True
ln (cumulative (Poisson 5.0) 8) ~~ -0.07052294
> True
ln (survivor (Poisson 5.0) 8) ~~ -2.686872
> True
quantile (Poisson 5.0) 0.7 == 6
> True
rand_vec 5 (\k. draw (Poisson 5.0) k) (new_key 0) :: Fin 5=>Nat
> [4, 4, 2, 2, 7]
-- uniform
ln (density (Uniform 2.0 5.0) 3.5) ~~ -1.098612
> True
ln (cumulative (Uniform 2.0 5.0) 3.5) ~~ -0.6931472
> True
ln (survivor (Uniform 2.0 5.0) 3.5) ~~ -0.6931472
> True
quantile (Uniform 2.0 5.0) 0.2 ~~ 2.6
> True
rand_vec 5 (\k. draw (Uniform 2.0 5.0) k) (new_key 0) :: Fin 5=>Float
> [4.610805, 2.740888, 2.510233, 3.040717, 3.731907]
-- data summaries
mean_and_variance [2.0,3.0,4.0] ~~ (3,1)
> True
variance [2.0,3.0,4.0] ~~ 1
> True
mean [2.0,3.0,4.0] ~~ 3.0
> True
variance [1.0,3.0,5.0] ~~ 4.0
> True
std_dev [1.0,3.0,5.0] ~~ 2.0
> True
mean_and_variance_matrix [[1.0,2.0],[3.0,4.0],[5.0,6.0]] ~~ ([3,4], [[4,4],[4,4]])
> True
mean [[1.0,2.0],[3.0,4.0],[5.0,6.0]] ~~ [3,4]
> True
variance_matrix [[1.0,2.0],[3.0,4.0],[5.0,6.0]] ~~ [[4,4],[4,4]]
> True
covariance [1.0,2.0,3.0] [2.0,3.0,4.0] ~~ 1
> True
covariance [1.0,2.0,3.0] [2.0,4.0,3.0] ~~ 0.5
> True
correlation [1.0,2.0,3.0] [2.0,4.0,3.0] ~~ 0.5
> True
covariance [1.0,2.0,3.0] [4.0,8.0,6.0] ~~ 1
> True
correlation [1.0,2.0,3.0] [4.0,8.0,6.0] ~~ 0.5
> True
variance_matrix (transpose [[1.0,2.0,3.0],[4.0,8.0,6.0]]) ~~ [[1,1],[1,4]]
> True
correlation_matrix (transpose [[1.0,2.0,3.0],[4.0,8.0,6.0]]) ~~ [[1,0.5],[0.5,1]]
> True
|
