How do you find the maximum likelihood estimator of a uniform distribution?

Maximum Likelihood Estimation (MLE) for a Uniform Distribution

1. Step 1: Write the likelihood function.
2. Step 2: Write the log-likelihood function.
3. Step 3: Find the values for a and b that maximize the log-likelihood by taking the derivative of the log-likelihood function with respect to a and b.

What is maximum likelihood statistics?

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable.

What does it mean to find the maximum likelihood estimate?

Maximum likelihood estimation is a method that determines values for the parameters of a model. The parameter values are found such that they maximise the likelihood that the process described by the model produced the data that were actually observed.

What is the likelihood of binomial distribution?

The Binomial distribution is the probability distribution that describes the probability of getting k successes in n trials, if the probability of success at each trial is p. This distribution is appropriate for prevalence data where you know you had k positive results out of n samples.

How do you find the likelihood?

The likelihood function is given by: L(p|x) ∝p4(1 − p)6. The likelihood of p=0.5 is 9.77×10−4, whereas the likelihood of p=0.1 is 5.31×10−5.

What is the method of maximum likelihood?

Is the maximum likelihood estimator consistent?

The maximum likelihood estimator (MLE) is one of the backbones of statistics, and common wisdom has it that the MLE should be, except in “atypical” cases, consistent in the sense that it converges to the true parameter value as the number of observations tends to infinity.

What is the maximum likelihood estimator for θ?

From the table we see that the probability of the observed data is maximized for θ=2. This means that the observed data is most likely to occur for θ=2. For this reason, we may choose ˆθ=2 as our estimate of θ. This is called the maximum likelihood estimate (MLE) of θ.

What is the likelihood of uniform distribution?

In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely. A deck of cards has within it uniform distributions because the likelihood of drawing a heart, a club, a diamond, or a spade is equally likely.