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0
votes
2answers
53 views

Maximum likelihood estimator based on 1 datum for non-canonical discrete distribution

One observation is taken from a discrete distribution with a parameter $\theta$. There are 3 possible values of $\theta$: 1, 2, and 3. The PMF is given below. What is the MLE of $\theta$? I ...
2
votes
0answers
134 views

Numerical optimization of discrete lognormal likelihood

Problem Template I am trying to numerically optimize a log likelihood function of the form: $$\displaystyle \mathcal{L}(\vec{x}) = -n\log\left(1-\mbox{erf}\left[ A(m-1) \right] \right) + \sum_{i=1}...
2
votes
0answers
38 views

Finding an MLE fit when a model predicts two kinds of data, each with a different distribution / data model

My problem is as follows: I am fitting some multi-parameter models which predict two different kinds of data. I can find a best (MLE) fit to the first kind of data. I'm currently expressing both the ...
0
votes
1answer
407 views

MLE for discrete uniform distribution [closed]

I am trying to find $N$ by MLE for several discrete uniform distributions involving a parmeter $N\in \mathbb{Z}$. If the interval $X$ is defined on is $X\in (N,N+1,...,N+10)$ then I think $\hat{N}=\...
5
votes
1answer
81 views

Finding quality of fit for two discrete variables with low statistics

I have data from an experiment which I am trying to explain using a model. I do not have an analytic formula for the prediction of the model but instead I got its prediction through a simulation. The ...
7
votes
1answer
2k views

Power-law fitting and testing

I want to test the distribution that best fit a specific metric (that I call SD) extracted from the source code of systems. I have a guess that they follow a power-law behavior. My sample: 20 systems ...
-1
votes
1answer
133 views

Find the maximum likelihood estimator of $\theta$

Let $(X_1,Y_1), . . . , (X_n,Y_n)$ be a random sample from the discrete distribution with joint probability mass function $$ f_{X,Y} (x,y) = \frac{\theta}4 , \space (x,y) = (0,0)\space or \space(1,1)...
2
votes
1answer
113 views

Distribution of MLE of $N$ based on a random sample of size n from discrete uniform dist.(1,2,…,$N$)

Let $X_1, X_2, ..., X_n$ be a random sample from discrete uniform distribution on $(1,2,\ldots,N)$, where $N$ is an unknown positive integer. Find MLE of $N$ and also find the distribution of the MLE. ...
3
votes
2answers
1k views

How to decide on the MLE when pmf is 0?

Suppose you have $\theta=\{1,2\}$ and the sample of (0,1,2) with the task of finding MLE: \begin{array} {|c|c|c|} \hline x & p(x|\theta=1) & p(x|\theta=2) \\ \hline 0 & 1/2 & 1/4 \\ \...
7
votes
1answer
475 views

Multinomial choice with binary observations

Is there a standard name for a multinomial choice model where the observations are in the form of binary questions such as "do you prefer A to B" and "do you prefer B to D"? This seems like a common ...