我有以下代码，我希望估计自定义分布的参数。 然后使用估计的参数，我想看看估计的PDF是否类似于给定数据的分布(它应该与给定数据的分布相匹配)。

[编辑]：'x'现在包含数据样本而不是PDF

主要代码是：

x = [0.0320000000000000 0.0280000000000000 0.0280000000000000 0.0270000000000000 0.0320000000000000 0.0320000000000000 0.0480000000000000 0.0890000000000000 0.0500000000000000 0.0620000000000000 0.0480000000000000 0.0300000000000000 0.0520000000000000 0.0460000000000000 0.0540000000000000 0.0520000000000000 0.0510000000000000 0.0310000000000000 0.0330000000000000 0.0330000000000000 0.0380000000000000 0.0850000000000000 0.102000000000000 0.0290000000000000 0.0530000000000000 0.0590000000000000 0.0320000000000000 0.0800000000000000 0.0410000000000000 0.0280000000000000 0.0670000000000000 0.0350000000000000 0.0420000000000000 0.0280000000000000 0.0370000000000000 0.0480000000000000 0.0330000000000000 0.101000000000000 0.0420000000000000 0.0840000000000000 0.0340000000000000 0.0900000000000000 0.0900000000000000 0.0460000000000000 0.0290000000000000 0.0330000000000000 0.0350000000000000 0.0330000000000000 0.0320000000000000 0.0420000000000000 0.0600000000000000 0.0500000000000000 0.0390000000000000 0.0480000000000000 0.0680000000000000 0.0330000000000000 0.0510000000000000 0.0430000000000000 0.0270000000000000 0.0330000000000000 0.0590000000000000 0.0380000000000000 0.0270000000000000 0.0600000000000000 0.0310000000000000 0.0520000000000000 0.0350000000000000 0.0640000000000000 0.0570000000000000 0.0520000000000000 0.0330000000000000 0.0480000000000000 0.0530000000000000 0.0380000000000000 0.0320000000000000 0.0340000000000000 0.0380000000000000 0.0470000000000000 0.0950000000000000 0.0510000000000000 0.0280000000000000 0.124000000000000 0.0360000000000000 0.0670000000000000 0.0380000000000000 0.0760000000000000 0.0440000000000000 0.0390000000000000 0.0500000000000000 0.0500000000000000 0.0370000000000000 0.0350000000000000 0.0490000000000000 0.0570000000000000 0.0560000000000000 0.0500000000000000 0.0350000000000000 0.0390000000000000 0.0390000000000000 0.0310000000000000 0.0260000000000000 0.0350000000000000 0.0610000000000000 0.0280000000000000 0.0480000000000000 0.0560000000000000 0.0650000000000000 0.0400000000000000 0.131000000000000 0.0600000000000000 0.0310000000000000 0.0620000000000000 0.0320000000000000 0.0510000000000000 0.0510000000000000 0.0480000000000000 0.0420000000000000 0.0470000000000000 0.0690000000000000 0.0590000000000000 0.0550000000000000 0.0580000000000000 0.0410000000000000 0.0320000000000000 0.0440000000000000 0.0370000000000000 0.0390000000000000 0.0620000000000000 0.0290000000000000 0.0340000000000000 0.0490000000000000 0.0300000000000000 0.0540000000000000 0.0420000000000000 0.0610000000000000 0.159000000000000 0.0520000000000000 0.0450000000000000 0.0670000000000000 0.0590000000000000 0.111000000000000 0.0250000000000000 0.0660000000000000 0.0210000000000000 0.0370000000000000 0.0330000000000000 0.0510000000000000 0.0330000000000000 0.0450000000000000 0.0530000000000000 0.0600000000000000 0.0400000000000000 0.0510000000000000 0.0680000000000000 0.0410000000000000 0.0490000000000000 0.0280000000000000 0.0520000000000000 0.0610000000000000 0.0390000000000000 0.0630000000000000 0.0360000000000000 0.0620000000000000 0.0550000000000000 0.0640000000000000 0.0650000000000000 0.0550000000000000 0.0480000000000000 0.0640000000000000 0.0850000000000000 0.0800000000000000 0.0390000000000000 0.0430000000000000 0.0380000000000000 0.0770000000000000 0.0620000000000000 0.0430000000000000 0.0490000000000000 0.0450000000000000 0.0510000000000000 0.0290000000000000 0.0440000000000000 0.0220000000000000 0.0400000000000000 0.0760000000000000 0.0290000000000000 0.0460000000000000 0.0450000000000000 0.0430000000000000 0.0790000000000000 0.0730000000000000 0.0660000000000000 0.0740000000000000 0.0330000000000000 0.0430000000000000 0.0450000000000000 0.0390000000000000 0.0610000000000000 0.0330000000000000 0.0480000000000000 0.0540000000000000 0.0400000000000000 0.0370000000000000 0.0350000000000000 0.0660000000000000 0.0280000000000000 0.0350000000000000 0.0500000000000000 0.0530000000000000 0.0370000000000000 0.0550000000000000 0.0390000000000000 0.0580000000000000 0.0220000000000000 0.0560000000000000 0.0440000000000000 0.0470000000000000 0.0390000000000000 0.0490000000000000 0.0640000000000000 0.0710000000000000 0.0510000000000000 0.0380000000000000 0.0480000000000000 0.0840000000000000 0.0430000000000000 0.0450000000000000 0.0370000000000000 0.0490000000000000 0.0390000000000000 0.0410000000000000 0.0440000000000000 0.0650000000000000 0.0470000000000000 0.0490000000000000 0.0480000000000000 0.0540000000000000 0.0680000000000000 0.0740000000000000 0.0350000000000000 0.0300000000000000 0.0450000000000000 0.0350000000000000 0.0370000000000000 0.0710000000000000 0.0360000000000000 0.0660000000000000 0.0380000000000000 0.0440000000000000 0.0320000000000000 0.0590000000000000 0.0390000000000000 0.0640000000000000 0.0630000000000000 0.0310000000000000 0.0570000000000000 0.0630000000000000 0.0280000000000000 0.0560000000000000 0.0910000000000000 0.0580000000000000 0.0680000000000000 0.0420000000000000 0.0810000000000000 0.0380000000000000 0.0250000000000000 0.0340000000000000 0.0450000000000000 0.0370000000000000 0.0390000000000000 0.0300000000000000 0.0410000000000000 0.0580000000000000 0.0300000000000000 0.0830000000000000 0.0380000000000000 0.0300000000000000 0.0530000000000000 0.0610000000000000 0.0370000000000000 0.0390000000000000 0.0340000000000000 0.0280000000000000 0.0420000000000000 0.0620000000000000 0.0520000000000000 0.0310000000000000 0.0590000000000000 0.0520000000000000 0.0420000000000000 0.0430000000000000 0.0410000000000000 0.0250000000000000 0.0570000000000000 0.0370000000000000 0.0270000000000000 0.0860000000000000 0.0660000000000000 0.0470000000000000 0.0270000000000000 0.0830000000000000 0.0440000000000000 0.0680000000000000 0.0500000000000000 0.0480000000000000 0.0520000000000000 0.0510000000000000 0.0290000000000000 0.0360000000000000 0.0290000000000000 0.0390000000000000 0.0290000000000000 0.0600000000000000 0.0310000000000000 0.0440000000000000 0.0410000000000000 0.0350000000000000 0.0510000000000000 0.0660000000000000 0.0450000000000000 0.0520000000000000 0.0530000000000000 0.0260000000000000 0.0690000000000000 0.0590000000000000 0.0760000000000000 0.118000000000000 0.0500000000000000 0.0480000000000000 0.0300000000000000 0.0300000000000000 0.0390000000000000 0.0340000000000000 0.0500000000000000 0.0280000000000000 0.0410000000000000 0.0490000000000000 0.0390000000000000 0.0390000000000000 0.0420000000000000 0.0520000000000000 0.0300000000000000 0.0320000000000000 0.0650000000000000 0.0650000000000000 0.0600000000000000 0.0450000000000000 0.0680000000000000 0.0350000000000000 0.0340000000000000 0.0260000000000000 0.0600000000000000 0.0920000000000000 0.0460000000000000 0.0560000000000000 0.0440000000000000 0.0450000000000000 0.0520000000000000 0.0480000000000000 0.0420000000000000 0.0990000000000000 0.0480000000000000 0.0360000000000000 0.0470000000000000 0.0390000000000000 0.0290000000000000 0.0270000000000000 0.0370000000000000 0.0580000000000000 0.0640000000000000 0.0300000000000000 0.0380000000000000 0.0240000000000000 0.0380000000000000 0.0830000000000000 0.0400000000000000 0.0990000000000000 0.0600000000000000 0.0580000000000000 0.0430000000000000 0.0840000000000000 0.0390000000000000 0.0370000000000000 0.0850000000000000 0.0590000000000000 0.0530000000000000 0.0560000000000000 0.0320000000000000 0.0340000000000000 0.0250000000000000 0.0520000000000000 0.0490000000000000 0.0270000000000000 0.0470000000000000 0.0520000000000000 0.0530000000000000 0.0410000000000000 0.0260000000000000 0.0290000000000000 0.0470000000000000 0.0550000000000000 0.0710000000000000 0.0520000000000000 0.0650000000000000 0.0440000000000000 0.0710000000000000 0.0550000000000000 0.0410000000000000 0.0640000000000000 0.0350000000000000 0.0930000000000000 0.0310000000000000 0.0480000000000000 0.0370000000000000 0.0380000000000000 0.0520000000000000 0.0370000000000000 0.0350000000000000 0.0280000000000000 0.0340000000000000 0.0400000000000000 0.0370000000000000 0.0570000000000000 0.0610000000000000 0.0440000000000000 0.0680000000000000 0.0470000000000000 0.0400000000000000 0.0270000000000000 0.0470000000000000 0.0350000000000000 0.0290000000000000 0.0280000000000000 0.0300000000000000 0.0770000000000000 0.0310000000000000 0.0560000000000000 0.0640000000000000 0.0420000000000000 0.0340000000000000 0.0290000000000000 0.0520000000000000 0.0260000000000000 0.0460000000000000 0.0380000000000000 0.0720000000000000 0.0750000000000000 0.0510000000000000 0.0560000000000000 0.0440000000000000 0.0390000000000000 0.0470000000000000 0.0450000000000000 0.0400000000000000 0.0880000000000000 0.0300000000000000 0.0440000000000000 0.0610000000000000 0.0370000000000000 0.0350000000000000 0.0490000000000000 0.0510000000000000 0.0820000000000000 0.0390000000000000 0.0440000000000000 0.0600000000000000 0.0310000000000000 0.0720000000000000 0.0460000000000000 0.0530000000000000 0.0500000000000000 0.0550000000000000 0.0390000000000000 0.0570000000000000 0.0460000000000000 0.0410000000000000 0.0470000000000000 0.0310000000000000 0.0720000000000000 0.0440000000000000 0.0610000000000000 0.0470000000000000 0.0420000000000000 0.0620000000000000 0.0790000000000000 0.0360000000000000 0.0450000000000000 0.0400000000000000 0.0540000000000000 0.0500000000000000 0.0430000000000000 0.0670000000000000 0.0230000000000000 0.0290000000000000 0.0450000000000000 0.0270000000000000 0.0470000000000000 0.0360000000000000 0.0600000000000000 0.0440000000000000 0.0290000000000000 0.0280000000000000 0.0350000000000000 0.0840000000000000 0.0660000000000000 0.0410000000000000 0.0300000000000000 0.0440000000000000 0.0450000000000000 0.0470000000000000 0.0620000000000000 0.0420000000000000 0.0300000000000000 0.0330000000000000 0.0320000000000000 0.0440000000000000 0.0700000000000000 0.0340000000000000 0.0420000000000000 0.0480000000000000 0.0360000000000000 0.0590000000000000 0.106000000000000 0.0280000000000000 0.0540000000000000 0.0870000000000000 0.0300000000000000 0.0300000000000000 0.0370000000000000 0.0210000000000000 0.0360000000000000 0.0910000000000000 0.126000000000000 0.0780000000000000 0.0510000000000000 0.0500000000000000 0.0370000000000000 0.0540000000000000 0.0380000000000000 0.0350000000000000 0.0480000000000000 0.0300000000000000 0.0340000000000000 0.133000000000000 0.0330000000000000 0.0340000000000000 0.0480000000000000 0.0590000000000000 0.0460000000000000 0.0650000000000000 0.0360000000000000 0.0650000000000000 0.0860000000000000 0.0290000000000000 0.0800000000000000 0.0430000000000000 0.0360000000000000 0.0490000000000000 0.0580000000000000 0.0310000000000000 0.0300000000000000 0.0330000000000000 0.0390000000000000 0.0330000000000000 0.0620000000000000 0.0330000000000000 0.0940000000000000 0.0270000000000000 0.0410000000000000 0.0570000000000000 0.0540000000000000 0.0390000000000000 0.0270000000000000 0.0590000000000000 0.0320000000000000 0.0390000000000000 0.0400000000000000 0.0720000000000000 0.0480000000000000 0.0480000000000000 0.0560000000000000 0.0730000000000000 0.0410000000000000 0.0520000000000000 0.0840000000000000 0.0590000000000000 0.0690000000000000 0.0330000000000000 0.0400000000000000 0.0320000000000000 0.0320000000000000 0.0310000000000000 0.0520000000000000 0.0760000000000000 0.0420000000000000 0.0370000000000000 0.0360000000000000 0.0780000000000000 0.0590000000000000 0.0390000000000000 0.0590000000000000 0.0880000000000000 0.0410000000000000 0.0640000000000000 0.0350000000000000 0.0350000000000000 0.0530000000000000 0.0490000000000000 0.0330000000000000 0.0640000000000000 0.0320000000000000 0.0880000000000000 0.0310000000000000 0.0980000000000000 0.0380000000000000 0.0270000000000000 0.0690000000000000 0.0530000000000000 0.0610000000000000 0.0380000000000000 0.0470000000000000 0.0620000000000000 0.0400000000000000 0.0400000000000000 0.0310000000000000 0.0740000000000000 0.0280000000000000 0.0310000000000000 0.0330000000000000 0.115000000000000 0.0890000000000000 0.0770000000000000 0.0490000000000000 0.0640000000000000 0.0580000000000000 0.0540000000000000 0.0330000000000000 0.0490000000000000 0.0230000000000000 0.0330000000000000 0.0490000000000000 0.0370000000000000 0.0330000000000000 0.0490000000000000 0.0460000000000000 0.0750000000000000 0.0420000000000000 0.0610000000000000 0.0340000000000000 0.0870000000000000 0.0390000000000000 0.0410000000000000 0.0430000000000000 0.0810000000000000 0.0570000000000000 0.0440000000000000 0.0470000000000000 0.0470000000000000 0.0320000000000000 0.0730000000000000 0.0590000000000000 0.0290000000000000 0.0450000000000000 0.0310000000000000 0.0450000000000000 0.0490000000000000 0.0880000000000000 0.0220000000000000 0.0330000000000000 0.0360000000000000 0.0350000000000000 0.0540000000000000 0.0470000000000000 0.0390000000000000 0.0300000000000000 0.0450000000000000 0.0740000000000000 0.0270000000000000 0.0320000000000000 0.0640000000000000 0.0750000000000000 0.0320000000000000 0.0300000000000000 0.0310000000000000 0.0470000000000000 0.0510000000000000 0.0520000000000000 0.0680000000000000 0.0700000000000000 0.0630000000000000 0.0410000000000000 0.0510000000000000 0.0460000000000000 0.0280000000000000 0.0780000000000000 0.0420000000000000 0.0390000000000000 0.0540000000000000 0.0310000000000000 0.0380000000000000 0.0320000000000000 0.0370000000000000 0.0260000000000000 0.0450000000000000 0.0610000000000000 0.0510000000000000 0.0240000000000000 0.0660000000000000 0.0380000000000000 0.0370000000000000 0.0450000000000000 0.0430000000000000 0.0710000000000000 0.0490000000000000 0.147000000000000 0.0340000000000000 0.0600000000000000 0.0400000000000000 0.0280000000000000 0.0350000000000000 0.0320000000000000 0.0410000000000000 0.0380000000000000 0.0380000000000000 0.0410000000000000 0.0600000000000000 0.0740000000000000 0.0350000000000000 0.0800000000000000 0.0370000000000000 0.0650000000000000 0.0300000000000000 0.0590000000000000 0.0620000000000000 0.0690000000000000 0.0540000000000000 0.0560000000000000 0.0230000000000000 0.0420000000000000 0.0560000000000000 0.0620000000000000 0.0460000000000000 0.0490000000000000 0.0690000000000000 0.0370000000000000 0.0400000000000000 0.0580000000000000 0.0340000000000000 0.0480000000000000 0.0300000000000000 0.0430000000000000 0.0270000000000000 0.0500000000000000 0.0550000000000000 0.0790000000000000 0.0380000000000000 0.0410000000000000 0.0450000000000000 0.0310000000000000 0.0430000000000000 0.0410000000000000 0.0480000000000000 0.0390000000000000 0.0650000000000000 0.0500000000000000 0.0500000000000000 0.0560000000000000 0.0690000000000000 0.0470000000000000 0.0790000000000000 0.0400000000000000 0.0540000000000000 0.0680000000000000 0.0660000000000000 0.0290000000000000 0.0520000000000000 0.0440000000000000 0.0570000000000000 0.0360000000000000 0.0610000000000000 0.0430000000000000 0.0470000000000000 0.0470000000000000 0.0500000000000000 0.0410000000000000 0.0690000000000000 0.0480000000000000 0.0480000000000000 0.0900000000000000 0.0590000000000000 0.0400000000000000 0.0340000000000000 0.0350000000000000 0.0520000000000000 0.0970000000000000 0.0350000000000000 0.0650000000000000 0.0320000000000000 0.0480000000000000 0.102000000000000 0.0410000000000000 0.0580000000000000 0.0260000000000000 0.0280000000000000 0.0660000000000000 0.0320000000000000 0.0390000000000000 0.0580000000000000 0.0450000000000000 0.0390000000000000 0.0610000000000000 0.0540000000000000 0.0490000000000000 0.0420000000000000 0.0490000000000000 0.0510000000000000 0.0350000000000000 0.0600000000000000 0.0920000000000000 0.0750000000000000 0.0360000000000000 0.0540000000000000 0.0850000000000000 0.0630000000000000 0.0330000000000000 0.0620000000000000 0.0370000000000000 0.0570000000000000 0.0280000000000000 0.0420000000000000 0.0510000000000000 0.0370000000000000 0.0480000000000000 0.125000000000000 0.0570000000000000 0.0870000000000000 0.0450000000000000 0.0310000000000000 0.0370000000000000 0.0650000000000000 0.0380000000000000 0.0590000000000000 0.0570000000000000 0.0540000000000000 0.0390000000000000 0.0500000000000000 0.0430000000000000 0.0360000000000000 0.0330000000000000 0.0280000000000000 0.0650000000000000 0.0440000000000000 0.0210000000000000 0.0410000000000000 0.0330000000000000 0.0600000000000000 0.0810000000000000 0.0370000000000000 0.0510000000000000 0.0370000000000000 0.0940000000000000 0.0440000000000000 0.0320000000000000 0.0590000000000000 0.0400000000000000 0.0570000000000000 0.0720000000000000 0.0640000000000000 0.0610000000000000 0.0500000000000000 0.0590000000000000 0.0520000000000000 0.0510000000000000 0.0910000000000000 0.0590000000000000 0.0370000000000000 0.0320000000000000 0.0740000000000000 0.0560000000000000 0.0310000000000000 0.0390000000000000 0.112000000000000 0.0580000000000000 0.0420000000000000 0.0280000000000000 0.0340000000000000 0.0360000000000000 0.0240000000000000 0.0380000000000000 0.0640000000000000 0.0320000000000000 0.0650000000000000 0.0300000000000000 0.0270000000000000 0.0530000000000000 0.0290000000000000 0.0380000000000000 0.0360000000000000 0.0510000000000000 0.0380000000000000 0.0340000000000000 0.0410000000000000 0.0630000000000000 0.0740000000000000 0.0760000000000000 0.0450000000000000 0.0630000000000000 0.0270000000000000 0.0660000000000000 0.0380000000000000 0.0540000000000000 0.0880000000000000 0.0450000000000000 0.0440000000000000 0.0460000000000000 0.0520000000000000 0.0380000000000000 0.0360000000000000 0.0500000000000000 0.0330000000000000 0.0610000000000000 0.0480000000000000 0.0480000000000000 0.0470000000000000 0.113000000000000 0.0470000000000000 0.0630000000000000 0.0800000000000000 0.0410000000000000 0.0630000000000000 0.0540000000000000 0.0450000000000000 0.0960000000000000 0.0500000000000000 0.0430000000000000 0.0340000000000000 0.0430000000000000 0.0440000000000000 0.0690000000000000 0.0580000000000000 0.0520000000000000 0.0640000000000000 0.0820000000000000 0.0390000000000000 0.0350000000000000 0.0700000000000000 0.0430000000000000 0.0340000000000000 0.0540000000000000 0.0580000000000000 0.0540000000000000 0.0430000000000000 0.0530000000000000 0.0590000000000000 0.0520000000000000 0.0730000000000000 0.0440000000000000 0.0970000000000000 0.0520000000000000 0.0510000000000000 0.0750000000000000 0.0320000000000000 0.0480000000000000 0.0410000000000000 0.0390000000000000 0.0380000000000000 0.0430000000000000 0.0440000000000000 0.0360000000000000 0.0400000000000000 0.0480000000000000 0.0430000000000000 0.0610000000000000 0.0610000000000000 0.0370000000000000 0.0520000000000000 0.0820000000000000 0.0480000000000000 0.0330000000000000 0.0460000000000000 0.0530000000000000 0.0690000000000000 0.0370000000000000 0.0330000000000000 0.0840000000000000 0.0860000000000000 0.0470000000000000 0.102000000000000 0.0350000000000000 0.0370000000000000 0.0630000000000000 0.0760000000000000 0.0830000000000000 0.0360000000000000 0.0590000000000000 0.0430000000000000 0.0790000000000000 0.0330000000000000 0.0520000000000000 0.0530000000000000];

Censored = ones(1,size(x,2));%

custpdf = @eval_custpdf;

custcdf = @eval_custcdf;

options = statset('Display','iter','MaxFunEvals',1000,'MaxIter',1000,...

'FunValCheck','off','TolX',1.0e-10,'TolFun',1.0e-10);

phat = mle(x,'pdf', custpdf,'cdf', custcdf,...

'start',[0.6,0.02,1.01,2,4,-10],...

'lowerbound',[0 0 0 0 0 -inf],...

'upperbound',[inf inf inf inf inf inf],...

'Censoring',Censored,...

'Options',options);;

% Checking how close the estimated PDF and CDF match with those from the data x

figure();

h = histogram(x,'Normalization','probability');hold on

x_times = h.BinEdges(1:end-1) + h.BinWidth/2 ;

y_vals = custpdf(x_times, phat(1), phat(2), phat(3), phat(4), phat(5), phat(6))./...

sum(custpdf(x_times, phat(1), phat(2), phat(3), phat(4), phat(5), phat(6)),'omitnan');

plot(x_times,y_vals,'linewidth',2)

legend('Data','Estimated PDF')

功能是：

function out = eval_custpdf(x,myalpha,mytheta,mybeta,a,b,c)

first_integral = integral(@(x) eval_K(x,a,b,c),0,1).^-1;

theta_t_ratio = (mytheta./x);

incomplete_gamma = igamma(myalpha,theta_t_ratio.^mybeta);

n_gamma = gamma(myalpha);

exponent_term = exp(-theta_t_ratio.^mybeta-(c.*(incomplete_gamma./n_gamma)));

numerator = first_integral.* mybeta.*incomplete_gamma.^(a-1).*...

theta_t_ratio.^(myalpha*mybeta+1).*exponent_term;

denominator = mytheta.* n_gamma.^(a+b-1).* (n_gamma-incomplete_gamma.^mybeta).^(1-b);

out = numerator./denominator;

end

function out = eval_custcdf(x,myalpha,mytheta,mybeta,a,b,c)

out = zeros(size(x));

for i = 1: length(x)

first_integral = integral(@(x) eval_K(x,a,b,c),0,1).^-1;

theta_t_ratio = mytheta./x(i);

incomplete_gamma = igamma(myalpha,theta_t_ratio.^mybeta);

n_gamma = gamma(myalpha);

second_integral = integral(@(x) eval_K(x,a,b,c),0,...

incomplete_gamma.^mybeta./n_gamma);

% second_integral = integral(@(x) eval_K(x,a,b,c),0,2);

out(i) = first_integral*second_integral;

end

end

function out = eval_K(x,a,b,c)

out = x.^(a-1).*(1-x).^(b-1).*exp(-c.*x);

end

但是，我没有成功获得所需的PDF。 如图所示，估计的PDF(橙色线)不会跟踪'x'(蓝色条)的直方图。

[更新]标准化直方图

请注意，我已经改变了参数的初始值。 但这非常耗时。 我还增加了迭代次数并最小化了容差，但还没有运气。 有没有更好的方法来估计除了mle之外的paratemters？

任何帮助，将不胜感激。

提前致谢。

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