def testEmpiricalUnimodalHpd1(self):
# Normal[mu=100, sd=1)
v = [100.93356, 100.66576, 99.44097, 100.60761, 103.65723, 101.15563,
99.09657, 100.39654, 98.77339, 101.13712, 99.33979, 99.99060,
100.39395, 101.68240, 100.99664, 99.17798, 100.83020, 98.90373,
100.30441, 99.49553, 100.52652, 99.76291, 99.95605, 99.63605,
99.21535, 100.51619, 100.55036, 101.21747, 101.04181, 97.76084,
100.19069, 99.46182, 100.47579, 99.56889, 100.23977, 101.22907,
97.85931, 100.86051, 99.56121, 100.44109, 100.02328, 98.62446,
100.11008, 100.12700, 99.27087, 100.72895, 99.06796, 99.38019,
99.79908, 100.82761, 101.26901, 99.88911, 98.09761, 99.16706,
98.98752, 100.10088, 100.58883, 99.42982, 101.90322, 101.22817,
101.36052, 97.70629, 100.15950, 99.39458, 100.19414, 103.43317,
100.32429, 98.90429, 101.28049, 99.82948, 100.96041, 99.46024,
98.22509, 101.63878, 100.66998, 101.82238, 99.49847, 100.41055,
98.71792, 99.66001, 98.53177, 99.11997, 100.14802, 98.96423,
101.93145, 100.09478, 100.85930, 99.82181, 101.50284, 99.93301,
99.57168, 98.19978, 100.90708, 99.25086, 101.74170, 99.86034,
99.85785, 99.89154, 99.62313, 99.41994,]
#==> 101.82238 97.70629
#==> 101.90322 97.76084
#==> 101.93145 97.85931
#==> 103.43317 98.09761
#==> 103.65723 98.19978
#n= 100
#nn= 5
#xx= [4.11609, 4.142380000000003, 4.0721400000000045, 5.335560000000001, 5.457449999999994]
#m= 4.07214
#nnn= 100
#(97.85931, 101.93145)
c1, c2 = statistics.empirical_hpd(v)
self.assertAlmostEqual(c1, 97.85931)
self.assertAlmostEqual(c2, 101.93145)
def testEmpiricalUnimodalHpd3(self):
# Gamma(shape=5.5, rate=100)
v = [
0.0380707918890542, 0.0613501755118962, 0.0349990175822757,
0.0619137725677135, 0.07861308334536, 0.0480553266749484,
0.062862553519841, 0.0682992193072175, 0.0498105967259703,
0.0391473475922808, 0.0814239076471267, 0.0622768940091115,
0.0278766690168117, 0.0317487156549716, 0.0586667309884353,
0.0610901783693829, 0.0614272435233303, 0.0467353725415623,
0.0235002000890242, 0.085772673901534, 0.0556214310452847,
0.0670344572022403, 0.0544400125583679, 0.0538488966212504,
0.05294861204774, 0.0487265157882631, 0.0319744057916896,
0.0727994868817337, 0.0406117459082881, 0.0411118268978343,
0.0500761307970585, 0.0308194535724841, 0.0657552493534245,
0.100523723943228, 0.0465808929090943, 0.0460932186699443,
0.0561270845816648, 0.0600098984413655, 0.039155736440776,
0.0477087458173384, 0.0662527620357706, 0.0259218058062224,
0.0240999453565313, 0.0403149976175261, 0.0397058239610132,
0.080726331847454, 0.084357840225122, 0.0469807175107997,
0.0629060978549567, 0.0815708340371883, 0.0662480716451838,
0.0291424513010887, 0.0423492520899737, 0.0400760974537379,
0.0988931209604346, 0.0334625360347498, 0.0481980311926021,
0.0326792585090408, 0.0454491423001323, 0.020993064627905,
0.0435735408306696, 0.0408747071998941, 0.0152619235644154,
0.0749659776042904, 0.0568986969556779, 0.0238240850033704,
0.0546832244279347, 0.0793788099421741, 0.0366737460311167,
0.0122826115173667, 0.0542719395504513, 0.0426583849776426,
0.0211571623626521, 0.097984660746214, 0.0909562231889738,
0.0317473196033018, 0.0683970866878872, 0.0249627875602813,
0.081633395263259, 0.050187713841904, 0.09452301382497,
0.0832417097555666, 0.0784842034909532, 0.0329463277742707,
0.134071786835307, 0.0672633924985841, 0.0492264776710421,
0.0346193998786818, 0.0608703914888914, 0.0479141586724897,
0.0653849788769291, 0.0363831431722953, 0.0978132293790966,
0.0663011935255327, 0.0245590323775349, 0.0438722027031532,
0.0294721189654155, 0.0482169372325583, 0.0372503987850244,
0.049380448859450
]
# n= 100
# nn= 5
# P1= 0.09781323 0.09798466 0.09889312 0.1005237 0.1340718
# P2= 0.01228261 0.01526192 0.02099306 0.02115716 0.0235002
# xx= 0.08553062 0.08272274 0.07790006 0.07936656 0.1105716
# m= 0.07790006
# nnn= 3
# FINAL = 0.02099306 0.09889312
# [1] 0.02099306 0.09889312
c1, c2 = statistics.empirical_hpd(v)
self.assertAlmostEqual(c1, 0.02099306)
self.assertAlmostEqual(c2, 0.09889312)
def testEmpiricalUnimodalHpd2(self):
# Exp(rate=0.2)
v = [3.27592276968062, 0.471030483022332, 8.69292160732502,
5.31655522508031, 11.6689748180798, 3.74156305545426,
0.930466635618359, 4.02394197251564, 0.0273082678142286,
2.19627505168319, 11.2686246344702, 3.12780772801489,
16.3526409110966, 1.03131624741206, 4.43873460812746,
1.16054141893983, 1.37002475326881, 4.03690286425358,
2.75003841612488, 0.247246073558927, 2.97294339863583,
9.91361622656596, 1.40643152873963, 5.06202565485096,
2.56700876867399, 5.10566710939115, 8.30197051456789,
0.439280721062038, 11.3532735680448, 1.46181986900046,
11.1246174474465, 2.24797004368156, 1.79919427493587,
8.79207140509944, 4.81857897692776, 2.30751369846985,
0.589188064119702, 3.36240844568238, 9.85515167894673,
13.7341997859286, 3.04674943210557, 10.2497380129517,
15.3365677214208, 0.322058985475451, 2.13952575810254,
8.7431202231924, 9.48776975232077, 0.437449288806399,
2.91444693226367, 0.234506344422698, 2.30315598892048,
11.9319818628238, 1.30209191970236, 1.34823656175286,
25.9922393489827, 9.88916845991366, 4.32954248951232,
0.748464160133153, 1.30975685780868, 10.16635726164,
12.2592059050905, 0.469188864149385, 1.23079363489524,
40.8792947675279, 5.14233190545297, 6.33412759730077,
4.14186116397752, 0.811017339583486, 2.73471124237403,
9.42033216315222, 6.48358419050878, 3.18536503706127,
3.99172384842717, 0.936779121402651, 9.05760801355255,
5.50938969922668, 1.06717714807019, 8.42135253320348,
3.84890870635814, 0.382886157387499, 6.31485156693912,
0.300180648919195, 0.8748722959183, 1.82131360052153,
3.14994857879356, 0.281196870910665, 7.2329476564647,
2.68667792435735, 0.364864277653396, 0.757411941885948,
5.50616672241545, 4.88404127282506, 0.167293788399547,
8.03142971525326, 10.5768193447809, 14.8404745685177,
1.30770040210336, 25.8265917826642, 1.59898946760222,
4.81477369067675,]
# n= 100
# nn= 5
# P1= 15.33657 16.35264 25.82659 25.99224 40.87929
# P2= 0.02730827 0.1672938 0.2345063 0.2472461 0.2811969
# xx= 15.30926 16.18535 25.59209 25.74499 40.5981
# m= 15.30926
# nnn= 1
# FINAL = 0.02730827 15.33657
# [1] 0.02730827 15.33656772
c1, c2 = statistics.empirical_hpd(v)
self.assertAlmostEqual(c1, 0.02730827)
self.assertAlmostEqual(c2, 15.33656772)
def testEmpiricalUnimodalHpd3(self):
# Gamma(shape=5.5, rate=100)
v = [0.0380707918890542, 0.0613501755118962, 0.0349990175822757,
0.0619137725677135, 0.07861308334536, 0.0480553266749484,
0.062862553519841, 0.0682992193072175, 0.0498105967259703,
0.0391473475922808, 0.0814239076471267, 0.0622768940091115,
0.0278766690168117, 0.0317487156549716, 0.0586667309884353,
0.0610901783693829, 0.0614272435233303, 0.0467353725415623,
0.0235002000890242, 0.085772673901534, 0.0556214310452847,
0.0670344572022403, 0.0544400125583679, 0.0538488966212504,
0.05294861204774, 0.0487265157882631, 0.0319744057916896,
0.0727994868817337, 0.0406117459082881, 0.0411118268978343,
0.0500761307970585, 0.0308194535724841, 0.0657552493534245,
0.100523723943228, 0.0465808929090943, 0.0460932186699443,
0.0561270845816648, 0.0600098984413655, 0.039155736440776,
0.0477087458173384, 0.0662527620357706, 0.0259218058062224,
0.0240999453565313, 0.0403149976175261, 0.0397058239610132,
0.080726331847454, 0.084357840225122, 0.0469807175107997,
0.0629060978549567, 0.0815708340371883, 0.0662480716451838,
0.0291424513010887, 0.0423492520899737, 0.0400760974537379,
0.0988931209604346, 0.0334625360347498, 0.0481980311926021,
0.0326792585090408, 0.0454491423001323, 0.020993064627905,
0.0435735408306696, 0.0408747071998941, 0.0152619235644154,
0.0749659776042904, 0.0568986969556779, 0.0238240850033704,
0.0546832244279347, 0.0793788099421741, 0.0366737460311167,
0.0122826115173667, 0.0542719395504513, 0.0426583849776426,
0.0211571623626521, 0.097984660746214, 0.0909562231889738,
0.0317473196033018, 0.0683970866878872, 0.0249627875602813,
0.081633395263259, 0.050187713841904, 0.09452301382497,
0.0832417097555666, 0.0784842034909532, 0.0329463277742707,
0.134071786835307, 0.0672633924985841, 0.0492264776710421,
0.0346193998786818, 0.0608703914888914, 0.0479141586724897,
0.0653849788769291, 0.0363831431722953, 0.0978132293790966,
0.0663011935255327, 0.0245590323775349, 0.0438722027031532,
0.0294721189654155, 0.0482169372325583, 0.0372503987850244,
0.049380448859450]
# n= 100
# nn= 5
# P1= 0.09781323 0.09798466 0.09889312 0.1005237 0.1340718
# P2= 0.01228261 0.01526192 0.02099306 0.02115716 0.0235002
# xx= 0.08553062 0.08272274 0.07790006 0.07936656 0.1105716
# m= 0.07790006
# nnn= 3
# FINAL = 0.02099306 0.09889312
# [1] 0.02099306 0.09889312
c1, c2 = statistics.empirical_hpd(v)
self.assertAlmostEqual(c1, 0.02099306)
self.assertAlmostEqual(c2, 0.09889312)
def testEmpiricalUnimodalHpd1(self):
# Normal[mu=100, sd=1)
v = [
100.93356,
100.66576,
99.44097,
100.60761,
103.65723,
101.15563,
99.09657,
100.39654,
98.77339,
101.13712,
99.33979,
99.99060,
100.39395,
101.68240,
100.99664,
99.17798,
100.83020,
98.90373,
100.30441,
99.49553,
100.52652,
99.76291,
99.95605,
99.63605,
99.21535,
100.51619,
100.55036,
101.21747,
101.04181,
97.76084,
100.19069,
99.46182,
100.47579,
99.56889,
100.23977,
101.22907,
97.85931,
100.86051,
99.56121,
100.44109,
100.02328,
98.62446,
100.11008,
100.12700,
99.27087,
100.72895,
99.06796,
99.38019,
99.79908,
100.82761,
101.26901,
99.88911,
98.09761,
99.16706,
98.98752,
100.10088,
100.58883,
99.42982,
101.90322,
101.22817,
101.36052,
97.70629,
100.15950,
99.39458,
100.19414,
103.43317,
100.32429,
98.90429,
101.28049,
99.82948,
100.96041,
99.46024,
98.22509,
101.63878,
100.66998,
101.82238,
99.49847,
100.41055,
98.71792,
99.66001,
98.53177,
99.11997,
100.14802,
98.96423,
101.93145,
100.09478,
100.85930,
99.82181,
101.50284,
99.93301,
99.57168,
98.19978,
100.90708,
99.25086,
101.74170,
99.86034,
99.85785,
99.89154,
99.62313,
99.41994,
]
#==> 101.82238 97.70629
#==> 101.90322 97.76084
#==> 101.93145 97.85931
#==> 103.43317 98.09761
#==> 103.65723 98.19978
#n= 100
#nn= 5
#xx= [4.11609, 4.142380000000003, 4.0721400000000045, 5.335560000000001, 5.457449999999994]
#m= 4.07214
#nnn= 100
#(97.85931, 101.93145)
c1, c2 = statistics.empirical_hpd(v)
self.assertAlmostEqual(c1, 97.85931)
self.assertAlmostEqual(c2, 101.93145)
def testEmpiricalUnimodalHpd2(self):
# Exp(rate=0.2)
v = [
3.27592276968062,
0.471030483022332,
8.69292160732502,
5.31655522508031,
11.6689748180798,
3.74156305545426,
0.930466635618359,
4.02394197251564,
0.0273082678142286,
2.19627505168319,
11.2686246344702,
3.12780772801489,
16.3526409110966,
1.03131624741206,
4.43873460812746,
1.16054141893983,
1.37002475326881,
4.03690286425358,
2.75003841612488,
0.247246073558927,
2.97294339863583,
9.91361622656596,
1.40643152873963,
5.06202565485096,
2.56700876867399,
5.10566710939115,
8.30197051456789,
0.439280721062038,
11.3532735680448,
1.46181986900046,
11.1246174474465,
2.24797004368156,
1.79919427493587,
8.79207140509944,
4.81857897692776,
2.30751369846985,
0.589188064119702,
3.36240844568238,
9.85515167894673,
13.7341997859286,
3.04674943210557,
10.2497380129517,
15.3365677214208,
0.322058985475451,
2.13952575810254,
8.7431202231924,
9.48776975232077,
0.437449288806399,
2.91444693226367,
0.234506344422698,
2.30315598892048,
11.9319818628238,
1.30209191970236,
1.34823656175286,
25.9922393489827,
9.88916845991366,
4.32954248951232,
0.748464160133153,
1.30975685780868,
10.16635726164,
12.2592059050905,
0.469188864149385,
1.23079363489524,
40.8792947675279,
5.14233190545297,
6.33412759730077,
4.14186116397752,
0.811017339583486,
2.73471124237403,
9.42033216315222,
6.48358419050878,
3.18536503706127,
3.99172384842717,
0.936779121402651,
9.05760801355255,
5.50938969922668,
1.06717714807019,
8.42135253320348,
3.84890870635814,
0.382886157387499,
6.31485156693912,
0.300180648919195,
0.8748722959183,
1.82131360052153,
3.14994857879356,
0.281196870910665,
7.2329476564647,
2.68667792435735,
0.364864277653396,
0.757411941885948,
5.50616672241545,
4.88404127282506,
0.167293788399547,
8.03142971525326,
10.5768193447809,
14.8404745685177,
1.30770040210336,
25.8265917826642,
1.59898946760222,
4.81477369067675,
]
# n= 100
# nn= 5
# P1= 15.33657 16.35264 25.82659 25.99224 40.87929
# P2= 0.02730827 0.1672938 0.2345063 0.2472461 0.2811969
# xx= 15.30926 16.18535 25.59209 25.74499 40.5981
# m= 15.30926
# nnn= 1
# FINAL = 0.02730827 15.33657
# [1] 0.02730827 15.33656772
c1, c2 = statistics.empirical_hpd(v)
self.assertAlmostEqual(c1, 0.02730827)
self.assertAlmostEqual(c2, 15.33656772)