Obtain maximum likelihood estimates

In summary, the conversation discusses using the Poisson distribution and a random sample to obtain maximum likelihood estimates for the average arrival rate of calls per hour. The request for reference material is made to aid in solving similar questions independently. A suggested reference is Wikipedia's entry on MLE and a link to a website detailing the procedure for common distributions is provided.
  • #1
TomJerry
50
0
Problem :
It is assumed that the arrival of the number of calls X per hour follow a poisson distribution with parameter [tex]\lambda[/tex], A random sample X1 = x1 , X2 = x2,...xn is taken .Obtain the maximum likelihood estimates of the average arrival rate.

Please can you provide me with some reference material so that i can solve such questions on my own .
 
Physics news on Phys.org
  • #2
TomJerry said:
Problem :
It is assumed that the arrival of the number of calls X per hour follow a poisson distribution with parameter [tex]\lambda[/tex], A random sample X1 = x1 , X2 = x2,...xn is taken .Obtain the maximum likelihood estimates of the average arrival rate.

Please can you provide me with some reference material so that i can solve such questions on my own .

Wikipedia's entry on MLE?
 
  • #3
Last edited:

1. What is the purpose of obtaining maximum likelihood estimates?

The purpose of obtaining maximum likelihood estimates is to determine the values of the parameters in a statistical model that are most likely to have produced the observed data. It is a method of estimation that is commonly used in statistical inference and is based on the likelihood function.

2. How do you calculate maximum likelihood estimates?

To calculate maximum likelihood estimates, you need to first specify a probability distribution that represents the data. Then, you use the observed data to calculate the likelihood function, which gives the probability of obtaining the observed data for a given set of parameter values. Finally, you use optimization techniques to find the parameter values that maximize the likelihood function.

3. What assumptions are necessary for obtaining maximum likelihood estimates?

There are a few assumptions that are necessary for obtaining maximum likelihood estimates. One is that the data are independent and identically distributed, meaning that each data point is independent and comes from the same probability distribution. Another is that the probability distribution chosen to represent the data is the correct one. Additionally, the data should be continuous and the likelihood function should be differentiable.

4. What are the advantages of using maximum likelihood estimates?

There are several advantages of using maximum likelihood estimates. One is that they are asymptotically efficient, meaning that as the sample size increases, the estimates will approach the true values of the parameters. Another advantage is that they are consistent, meaning that as the sample size increases, the estimates will converge to the true values. Additionally, maximum likelihood estimates have strong theoretical properties and are widely used in statistical inference.

5. Are there any limitations to using maximum likelihood estimates?

Yes, there are some limitations to using maximum likelihood estimates. One is that they can be sensitive to outliers, meaning that extreme data points can heavily influence the estimates. Another limitation is that they can be biased, meaning that the estimates may not accurately reflect the true values of the parameters. Additionally, maximum likelihood estimates may not be feasible for complex models or large datasets, as they can be computationally intensive.

Similar threads

I Maximum likelihood to fit a parameter of this model
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
I What Does the Likelihood Function Tell Us?
    • Set Theory, Logic, Probability, Statistics
Replies
16
Views
1K
MHB Finding MLE for $\theta$ of Statistical Product Model
    • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
I Why is the maximum likelihood estimation accurate?
    • Set Theory, Logic, Probability, Statistics
Replies
11
Views
2K
I Maximum Likelihood to find the original data or estimation directly
    • Set Theory, Logic, Probability, Statistics
Replies
8
Views
1K
MHB Likelihood Ratio Test for Common Variance from Two Normal Distribution Samples
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
925
MHB Maximum Likelihood Estimators for Uniform Distribution
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
2K
MHB Binomial Distribution: Likelihood Ratio Test for Equality of Several Proportions
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K
I What to do with biased estimators if we don't know the bias term?
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
446
I Desirable estimator properties...
    • Set Theory, Logic, Probability, Statistics
Replies
7
Views
475

Hot Threads

Recent Insights

Back
Top