i have a custom distribution and data as follow

 i={42, 180, 35, 392, 63, 230, 112, 281, 42, 28, 42, 120, 148, 16, 310, 28, 68, 336, 21.5, 50, 19, 30, 12, 120, 140, 170, 17, 115, 31, 21,  52, 164, 225, 225, 151, 60, 200, 46, 210, 14};
MO = ProbabilityDistribution[{"CDF",  1 - ((\[Alpha]*E^-x)/(1 - (1 - \[Alpha])*E^-x))}, {x,  0, \[Infinity]}, Assumptions -> {\[Alpha] > 0}]

i used maximum likelihood as follow

mlmo = FindDistributionParameters[i, MO, ParameterEstimator -> "MaximumLikelihood"]

and the output was as follow

{\[Alpha] -> 4.57761*10^7}

when i used loglikelihood as follow the results was as follow

LogLikelihood[MO, {42, 180, 35, 392, 63, 230, 112, 281, 42, 28, 42, 120, 148, 16, 310, 28, 68, 336, 21.5, 50, 19, 30, 12, 120, 140, 170, 17, 115, 31, 21, 52, 164, 225, 225, 151, 60, 200, 46, 210,  14}] /.  {\[Alpha] -> 4.57761*10^7}

the output was

-3885.87

i used this code and wrote log likelihood manual to get parameter

bbb = Total[logpdf = (Log[PDF[MOE, i]])]
Dbal = D[bbb, \[Alpha]]
b = FindRoot[Dbal, {\[Alpha], 1}]

and this the output  

and the loglikelihood

LogLikelihood[MOE, {42, 180, 35, 392, 63, 230, 112, 281, 42, 28, 42, 120, 148, 16,310, 28, 68, 336, 21.5, 50, 19, 30, 12, 120, 140, 170, 17, 115,  31, 21, 52, 164, 225, 225, 151, 60, 200, 46, 210, 14}] /. {\[Alpha] -> 2.2402116078266955`*^21}

and the output is better

-3283.72

now i don't know the output means?

I have a custom distribution and data as follows

 i={42, 180, 35, 392, 63, 230, 112, 281, 42, 28, 42, 120, 148, 16, 310, 28, 68, 336, 21.5, 50, 19, 30, 12, 120, 140, 170, 17, 115, 31, 21,  52, 164, 225, 225, 151, 60, 200, 46, 210, 14};
MO = ProbabilityDistribution[{"CDF",  1 - ((\[Alpha]*E^-x)/(1 - (1 - \[Alpha])*E^-x))}, {x,  0, \[Infinity]}, Assumptions -> {\[Alpha] > 0}]

i used maximum likelihood as follow

mlmo = FindDistributionParameters[i, MO, ParameterEstimator -> "MaximumLikelihood"]

and the output was as follows

{\[Alpha] -> 4.57761*10^7}

When I used loglikelihood as follow the results was as follows

LogLikelihood[MO, {42, 180, 35, 392, 63, 230, 112, 281, 42, 28, 42, 120, 148, 16, 310, 28, 68, 336, 21.5, 50, 19, 30, 12, 120, 140, 170, 17, 115, 31, 21, 52, 164, 225, 225, 151, 60, 200, 46, 210,  14}] /.  {\[Alpha] -> 4.57761*10^7}

The output was -3885.87. I used this code and wrote log likelihood manual to get parameter

bbb = Total[logpdf = (Log[PDF[MOE, i]])]
Dbal = D[bbb, \[Alpha]]
b = FindRoot[Dbal, {\[Alpha], 1}]

This the output 

This is the loglikelihood

LogLikelihood[MOE, {42, 180, 35, 392, 63, 230, 112, 281, 42, 28, 42, 120, 148, 16,310, 28, 68, 336, 21.5, 50, 19, 30, 12, 120, 140, 170, 17, 115,  31, 21, 52, 164, 225, 225, 151, 60, 200, 46, 210, 14}] /. {\[Alpha] -> 2.2402116078266955`*^21}

The output is better: -3283.72 Now, what does the output mean?