# Can you really solve for an MLE given a fictitious distributi

#### idejstark

##### New Member
to estimate MLE, you need more than one observation, right? What if you don't have a density function? (It's a fictitious disitrubtion)

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#### BioStatMatt

##### TS Contributor
In order to form a maximum likelihood estimate (MLE), you must have a likelihood function. If $$y_1, \ldots, y_n \sim f(y_i|\theta)$$, where $$f(y_i|\theta)$$ is a density function indexed by $$\theta$$, then the likelihood function is given by $$L(\theta|y_1,\ldots,y_n) = \prod_{i=1}^n f(y_i|\theta)$$. Of course, without an explicit density function, we can't go much farther than this in computing an MLE.

In general, no more than one observation is required in order to compute a MLE. However, the MLE may not be unique. This problem is called unidentifiability. That is, when there are few observations, the MLE may be a poor estimate of $$\theta$$.

#### fed1

##### TS Contributor
Just to be totally confusing I wan to point out that there is
non parametric maximum liklihood (MELE) that leads to k-m and empirical cdf. Not alot to say about one observation though!! :yup:

#### Ksharp

##### New Member
BioStatMatt is correct.
Without disitrubtion function , cann't get maximum likelihood estimate .
But for k-m , using empirical distribution , it would be better with more observations.