import ROOT def loglikelihood(counts,rate,err_rate,duration,efficiency,err_eff): def func(params): """ params[0] : normalization params[1] : rate params[2] : efficiency """ loglike = 0 for i in range(len(counts)): exp = params[0]*params[1][i]*duration*params[2][i] pois = ROOT.Math.poisson_pdf(int(counts[i]),exp) if pois >0: loglike += ROOT.TMath.Log(pois) else: loglike+=1e7 gaus_eff = ROOT.Math.gaussian_pdf(params[2][i],efficiency[i],err_eff[i]) if gaus_eff >0: loglike += ROOT.TMath.Log(gaus_eff) else: loglike+=1e7 gaus_rate = ROOT.Math.gaussian_pdf(params[1][i],rate[i],err_rate[i]) if gaus_rate >0: loglike += ROOT.TMath.Log(gaus_rate) else: loglike+=1e7 return -2*loglike nparams = 2*len(counts)+1 return func,nparams def loglikelihoodfit(func, nparams, parvals=None, parranges=None, parnames=None, minName='Minuit2', algoName=""): fcn = ROOT.Math.Functor(func, nparams) fitter = ROOT.Fit.Fitter() SetStatus = fitter.SetFCN(fcn) if not SetStatus: print("Failed to set the function.") return None if parnames is None: parnames={} for i in range(nparams): label = f'p{i}' if i in parnames: label = parnames[i] fitter.Config().ParSettings(i).SetName(label) FitStatus = fitter.FitFCN() if not FitStatus: print("Fit Failed") return None res = fitter.Result() return res meas_counts=[2.07914e+05, 3.14400e+03, 7.00000e+02, 2.84000e+02, 1.65000e+02, 7.60000e+01, 4.80000e+01, 4.00000e+01, 3.00000e+01, 3.00000e+01, 2.60000e+01, 2.20000e+01, 1.40000e+01, 2.10000e+01, 1.60000e+01, 1.10000e+01, 9.00000e+00, 9.00000e+00, 1.30000e+01, 1.20000e+01, 1.00000e+01, 1.40000e+01, 1.00000e+01, 9.00000e+00, 8.00000e+00, 6.00000e+00, 8.00000e+00, 8.00000e+00, 3.00000e+00, 4.00000e+00, 7.00000e+00, 1.00000e+01, 2.00000e+00, 8.00000e+00, 2.00000e+00, 1.00000e+01, 7.00000e+00, 5.00000e+00, 7.00000e+00, 5.00000e+00, 3.00000e+00, 5.00000e+00, 1.00000e+01, 4.00000e+00, 4.00000e+00, 2.00000e+00, 4.00000e+00, 3.00000e+00, 2.00000e+00, 4.00000e+00, 3.00000e+00, 3.00000e+00, 1.00000e+00, 5.00000e+00, 2.00000e+00, 3.00000e+00, 1.00000e+00, 2.00000e+00, 3.00000e+00, 1.00000e+00, 7.00000e+00, 4.00000e+00, 1.00000e+00, 1.00000e+00, 2.00000e+00, 2.00000e+00, 4.00000e+00, 3.00000e+00, 1.00000e+00, 2.00000e+00, 1.00000e+00, 0.00000e+00, 5.00000e+00, 4.00000e+00, 2.00000e+00, 3.00000e+00, 2.00000e+00, 0.00000e+00, 1.00000e+00, 2.00000e+00, 6.00000e+00, 1.00000e+00, 3.00000e+00, 5.00000e+00, 3.00000e+00, 0.00000e+00, 2.00000e+00, 2.00000e+00, 1.00000e+00, 3.00000e+00, 6.00000e+00, 1.00000e+00, 3.00000e+00, 1.00000e+00, 0.00000e+00, 1.00000e+00, 0.00000e+00, 4.00000e+00, 3.00000e+00, 4.00000e+00, 0.00000e+00, 2.00000e+00, 1.00000e+00, 1.00000e+00, 1.00000e+00, 3.00000e+00, 0.00000e+00, 2.00000e+00, 2.00000e+00, 4.00000e+00, 3.00000e+00, 1.00000e+00, 3.00000e+00, 2.00000e+00, 2.00000e+00, 2.00000e+00, 1.00000e+00, 3.00000e+00, 1.00000e+00, 2.00000e+00, 0.00000e+00, 1.00000e+00, 2.00000e+00, 4.00000e+00, 4.00000e+00, 3.00000e+00, 1.00000e+00, 1.00000e+00, 4.00000e+00, 0.00000e+00, 3.00000e+00, 2.00000e+00, 2.00000e+00, 4.00000e+00, 2.00000e+00, 3.00000e+00, 1.00000e+00, 4.00000e+00, 4.00000e+00, 2.00000e+00, 1.00000e+00, 2.00000e+00, 3.00000e+00, 1.00000e+00, 3.00000e+00, 2.00000e+00, 2.00000e+00, 1.00000e+00, 1.00000e+00, 2.00000e+00, 1.00000e+00, 0.00000e+00, 2.00000e+00, 3.00000e+00, 1.00000e+00, 6.00000e+00, 3.00000e+00, 6.00000e+00, 1.00000e+00, 3.00000e+00, 1.00000e+00, 1.00000e+00, 1.00000e+00, 1.00000e+00, 4.00000e+00, 0.00000e+00, 1.00000e+00, 2.00000e+00, 2.00000e+00, 2.00000e+00, 4.00000e+00, 1.00000e+00, 5.00000e+00, 1.00000e+00, 4.00000e+00, 2.00000e+00, 4.00000e+00, 3.00000e+00, 4.00000e+00, 3.00000e+00, 1.00000e+00, 1.00000e+00, 4.00000e+00, 4.00000e+00, 3.00000e+00, 1.00000e+00, 0.00000e+00, 1.00000e+00, 0.00000e+00, 2.00000e+00, 4.00000e+00, 3.00000e+00, 1.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 1.00000e+00, 1.00000e+00, 0.00000e+00, 1.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00] exp_rate = [0.0635626 , 0.04740006, 0.04047559, 0.05115633, 0.02086318, 0.1031579 , 0.04169234, 0.05168026, 0.03460627, 0.04065441, 0.04033088, 0.03597722, 0.02220676, 0.02741189, 0.03210919, 0.02283993, 0.01742011, 0.01957957, 0.03554783, 0.03447283, 0.02434531, 0.00467207, 0.07471817, 0.06897069, 0.02255702, 0.02923248, 0.04156569, 0.04332393, 0.0507813 , 0.0440198 , 0.05454809, 0.0570828 , 0.03566992, 0.01410516, 0.07605759, 0.02825942, 0.03307539, 0.03066684, 0.05822966, 0.04521386, 0.04568763, 0.00784687, 0.01185518, 0.0281504 , 0.04911298, 0.03276735, 0.02229787, 0.03865495, 0.01837567, 0.03333622, 0.0306063 , 0.04309129, 0.01726605, 0.05848879, 0.04340514, 0.039172 , 0.05559085, 0.04965925, 0.0497478 , 0.04369979, 0.03145105, 0.03705106, 0.03814378, 0.04841874, 0.0322569 , 0.03398314, 0.04894494, 0.03292415, 0.0375475 , 0.0455243 , 0.03845066, 0.04468348, 0.03466425, 0.05600959, 0.03726527, 0.06423618, 0.0865993 , 0.03667581, 0.07737593, 0.0415975 , 0.05794754, 0.03126112, 0.06895451, 0.01081375, 0.02659674, 0.0477702 , 0.04162693, 0.02447072, 0.00582356, 0.02449889, 0.06880492, 0.01815125, 0.05942088, 0.0427411 , 0.03762974, 0.0389627 , 0.04847999, 0.02887519, 0.03210937, 0.05698302, 0.07007875, 0.04076768, 0.03027806, 0.0313923 , 0.03152634, 0.01855677, 0.02856149, 0.03472159, 0.00446751, 0.04558219, 0.03850082, 0.01223826, 0.03443143, 0.03178761, 0.06809013, 0.06453538, 0.05871544, 0.02376645, 0.02716408, 0.04674467, 0.03262925, 0.02606126, 0.04206898, 0.05217626, 0.03792 , 0.02735688, 0.02288691, 0.02120666, 0.04580953, 0.01999294, 0.06764128, 0.01909269, 0.05315785, 0.06608396, 0.0267314 , 0.08355416, 0.0454885 , 0.02439451, 0.01710991, 0.03155962, 0.02914549, 0.0246386 , 0.0245522 , 0.02433587, 0.02585896, 0.04783398, 0.03035415, 0.06427175, 0.01224084, 0.01977881, 0.03481975, 0.02991084, 0.0337163 , 0.03774938, 0.01830768, 0.05578025, 0.05068826, 0.0348872 , 0.03381498, 0.01481279, 0.04952758, 0.032675 , 0.05256039, 0.04350085, 0.02896997, 0.02406046, 0.05554632, 0.02256609, 0.00319576, 0.03664544, 0.0170515 , 0.02155972, 0.04722373, 0.07208294, 0.03945534, 0.06155634, 0.04798413, 0.05267582, 0.02085835, 0.04255174, 0.02286321, 0.04759915, 0.01402018, 0.02632928, 0.04703806, 0.05464922, 0.07768663, 0.03687194, 0.01304395, 0.04255925, 0.0407749 , 0.04199519, 0.0256526 , 0.03201405, 0.02632585, 0.00459957, 0.01746946, 0.0774727 , 0.01817982, 0.02400782, 0.00594499, 0.01813179, 0.05122672, 0.03558612, 0.05092612, 0.03256803, 0.05890648, 0.02064805, 0.05450051, 0.05594297, 0.01283229, 0.05961917, 0.04121545, 0.05596562, 0.02325248, 0.02959797, 0.02592765, 0.04243465, 0.06259775, 0.01349551, 0.01201782, 0.0233364 , 0.06239506, 0.02072911, 0.06119045, 0.04788318, 0.03331381, 0.02503707, 0.01611218, 0.02849454, 0.01439844, 0.02729068, 0.03853021, 0.01109324, 0.04240626, 0.06592522, 0.03428844, 0.04225842, 0.05953072, 0.04250974, 0.05846891, 0.02168527, 0.02593987, 0.02510053, 0.02919091, 0.04218839, 0.04623761, 0.01917489] error_rate = [0.02314516, 0.01927105, 0.01832185, 0.02047191, 0.0110481 , 0.03080148, 0.0183247 , 0.0205041 , 0.01839944, 0.02074369, 0.01829025, 0.01614006, 0.01119551, 0.01608572, 0.01594323, 0.00996555, 0.00979934, 0.0099116 , 0.01621778, 0.01606097, 0.01307061, 0.00133858, 0.02610907, 0.02425488, 0.01299864, 0.01426145, 0.01837655, 0.01842023, 0.02049203, 0.01861231, 0.02067951, 0.02071472, 0.01606904, 0.00925104, 0.02613348, 0.01339159, 0.01594598, 0.0158334 , 0.02088965, 0.01870477, 0.02147847, 0.00290045, 0.00914778, 0.01346865, 0.01934635, 0.01648901, 0.01297388, 0.016951 , 0.00985878, 0.01464807, 0.01701623, 0.01674587, 0.00950158, 0.02101601, 0.02054277, 0.01860341, 0.02080362, 0.02046153, 0.01944152, 0.01848339, 0.01645704, 0.01566297, 0.01860163, 0.02079277, 0.01380471, 0.0146883 , 0.02043707, 0.01597809, 0.01612922, 0.02063284, 0.01859966, 0.02055015, 0.01542962, 0.02127489, 0.01657009, 0.02315265, 0.02813078, 0.01850004, 0.02468196, 0.0183767 , 0.02147546, 0.01513164, 0.02282994, 0.00370025, 0.01327215, 0.02070803, 0.0194092 , 0.01313114, 0.00235739, 0.01321946, 0.02338608, 0.01315944, 0.02242559, 0.01842067, 0.01633392, 0.01704507, 0.01971375, 0.01438112, 0.01595163, 0.02095208, 0.02454507, 0.01828339, 0.01583231, 0.01586552, 0.01583689, 0.00980807, 0.01371959, 0.01840059, 0.00199599, 0.02063532, 0.01704064, 0.00437896, 0.01598774, 0.01455256, 0.02330032, 0.024449 , 0.02276699, 0.01326344, 0.01613333, 0.01879613, 0.01595487, 0.01327323, 0.02082585, 0.02148278, 0.01694008, 0.01264983, 0.01138786, 0.0129304 , 0.01954649, 0.01006418, 0.02337224, 0.01011987, 0.02068187, 0.02131174, 0.01346245, 0.02760753, 0.01875459, 0.01326657, 0.00967173, 0.01701921, 0.01360327, 0.01321431, 0.01312304, 0.01313148, 0.01173153, 0.01804841, 0.01376714, 0.0246953 , 0.00915951, 0.01103873, 0.01840394, 0.01451468, 0.01461364, 0.01852768, 0.01342717, 0.02267849, 0.02268661, 0.01478637, 0.0183984 , 0.00942078, 0.02046417, 0.01875806, 0.0206504 , 0.01852595, 0.01619451, 0.01326541, 0.02339101, 0.01125717, 0.00049457, 0.01689324, 0.00703644, 0.01020404, 0.02068478, 0.02627504, 0.01714794, 0.02156343, 0.01874872, 0.02061318, 0.0129285 , 0.01735947, 0.01307044, 0.01649357, 0.00935911, 0.01341358, 0.01929281, 0.02256545, 0.02472916, 0.01854394, 0.00921171, 0.01841888, 0.01873798, 0.01851788, 0.01325113, 0.01594256, 0.01346239, 0.00200874, 0.00972428, 0.02588486, 0.00996373, 0.01307596, 0.00273685, 0.00986615, 0.01995491, 0.01604749, 0.02274712, 0.01594938, 0.02150559, 0.0101674 , 0.02256789, 0.02175329, 0.00924391, 0.02248001, 0.01872932, 0.02094839, 0.01379545, 0.01352718, 0.0134077 , 0.01660717, 0.02256952, 0.00933657, 0.00914961, 0.01307287, 0.02429552, 0.01111635, 0.0225613 , 0.02071809, 0.01610811, 0.01318803, 0.01310584, 0.01425891, 0.00936504, 0.01425511, 0.01646156, 0.00914376, 0.01851861, 0.02322734, 0.01608012, 0.01841507, 0.02454081, 0.01678922, 0.02443718, 0.01008185, 0.01340086, 0.0133081 , 0.01438377, 0.01852068, 0.01871806, 0.010121 ] effi = [0.40876416, 0.86177255, 0.95726565, 0.98577473, 0.98668223, 0.99032219, 0.99025826, 0.98792266, 0.98666173, 0.98565027, 0.98493633, 0.9849608 , 0.98512401, 0.98535062, 0.98561382, 0.98587273, 0.9861225 , 0.98631153, 0.98648237, 0.98665316, 0.98682385, 0.98678221, 0.98633025, 0.98429342, 0.98139244, 0.97610061, 0.97167175, 0.96913546, 0.97507537, 0.9791716 , 0.98190384, 0.98303418, 0.98398506, 0.98473297, 0.98498644, 0.98519632, 0.9854415 , 0.98552216, 0.9855593 , 0.98560426, 0.98579483, 0.9860449 , 0.98633886, 0.98663285, 0.98702129, 0.98762684, 0.98838825, 0.98919511, 0.98998664, 0.99134749, 0.99308105, 0.99328767, 0.99181429, 0.98890057, 0.98685658, 0.98528176, 0.9843631 , 0.98407819, 0.98390969, 0.98383689, 0.98382637, 0.98401469, 0.98468303, 0.98532172, 0.98596428, 0.9866601 , 0.98685431, 0.98682859, 0.98661325, 0.98639776, 0.98618215, 0.98596632, 0.98529853, 0.98417458, 0.98172766, 0.97866114, 0.97502356, 0.97565518, 0.97715452, 0.97940213, 0.98124665, 0.98280945, 0.98406497, 0.98470674, 0.98519091, 0.98536514, 0.98553949, 0.98574277, 0.98606417, 0.98647657, 0.98693541, 0.98739456, 0.98794143, 0.98856713, 0.98949096, 0.99041518, 0.99133977, 0.99226511, 0.9931908 , 0.99411691, 0.99504372, 0.99535343, 0.99470396, 0.99389909, 0.99310071, 0.99230252, 0.99150458, 0.99070678, 0.98990919, 0.98911183, 0.98831462, 0.98751764, 0.98672087, 0.98592424, 0.98512786, 0.98433168, 0.98353563, 0.98273986, 0.98194426, 0.9811488 , 0.98035364, 0.97955862, 0.97876376, 0.97796919, 0.97717475, 0.9763805 , 0.97558651, 0.9750474 , 0.97504689, 0.97551234, 0.97610357, 0.97669491, 0.97728637, 0.97787791, 0.97846958, 0.97906135, 0.9796532 , 0.98024519, 0.98083727, 0.98142943, 0.98202174, 0.98261413, 0.9832066 , 0.98379923, 0.98439193, 0.98498472, 0.98557766, 0.98617067, 0.98676378, 0.98735703, 0.98795025, 0.98854336, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571, 0.98868571] err_effi = [0.00101315, 0.00205838, 0.00159786, 0.00147248, 0.00159796, 0.00108873, 0.00121587, 0.00171224, 0.002006 , 0.00225096, 0.00243654, 0.00244157, 0.00239971, 0.00233435, 0.00224882, 0.00217305, 0.00211962, 0.00208758, 0.00206197, 0.00203637, 0.00201079, 0.00201605, 0.00207581, 0.00234535, 0.00271838, 0.00337208, 0.00392753, 0.00425049, 0.0035701 , 0.00312338, 0.00284197, 0.00276171, 0.0026985 , 0.00265418, 0.00265572, 0.00265677, 0.00264389, 0.00263656, 0.00263433, 0.00262832, 0.00260736, 0.00258431, 0.00257088, 0.00255745, 0.00253471, 0.00248657, 0.00242183, 0.00235183, 0.00228941, 0.00220069, 0.00209908, 0.00212747, 0.00229716, 0.00258331, 0.00279055, 0.00295396, 0.00305513, 0.00307888, 0.00308899, 0.00308893, 0.00308307, 0.0030586 , 0.00298919, 0.0029183 , 0.00284384, 0.00275777, 0.00271815, 0.00269187, 0.00268292, 0.00267401, 0.00266514, 0.00265632, 0.00270261, 0.00280069, 0.00304298, 0.00337649, 0.00380208, 0.00376127, 0.00362842, 0.00341537, 0.00323357, 0.00307437, 0.00293976, 0.00285971, 0.00279897, 0.00277898, 0.00275897, 0.00273675, 0.00270555, 0.00266753, 0.00262603, 0.00258445, 0.00253313, 0.00247296, 0.00237824, 0.00228342, 0.00218852, 0.00209344, 0.00199828, 0.00190302, 0.00180759, 0.00177468, 0.00183871, 0.00192671, 0.00201494, 0.00210314, 0.00219131, 0.00227946, 0.00236757, 0.00245565, 0.00254372, 0.00263175, 0.00271975, 0.00280772, 0.00289567, 0.00298358, 0.00307148, 0.00315933, 0.00324716, 0.00333497, 0.00342274, 0.00351049, 0.00359822, 0.0036859 , 0.00377356, 0.0038612 , 0.0039488 , 0.00400944, 0.00401303, 0.00396704, 0.00390765, 0.00384823, 0.00378881, 0.00372937, 0.00366992, 0.00361046, 0.00355099, 0.0034915 , 0.00343199, 0.00337248, 0.00331295, 0.00325341, 0.00319386, 0.00313429, 0.00307472, 0.00301513, 0.00295552, 0.0028959 , 0.00283627, 0.00277663, 0.00271698, 0.00265735, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304, 0.00264304] duration = 23.833391203703705 #generate the likelihood function min_func,nparams = loglikelihood(meas_counts, exp_rate, error_rate, duration, effi, err_effi ) #perform minimization res = loglikelihoodfit(min_func,nparams)