Simulating bivariate distribution?

In summary, the conversation discusses how to simulate a random variable with a given distribution using uniformly distributed variables. It also provides steps for simulating a 1-dimensional pdf and using it to check homework answers.
  • #1
zli034
107
0
Hi:

From the undergraduate study we know that if we want to simulate a random variable x with distribution Fx(x). We just make Fx(x)=u, u is a uniform distributed variable, find Fx inverse of U. Then we just need to plugin u the uniform distributed random variable.

How about we have Fxy(x,y). How do we simulate this distribution if we only have uniformly distributed variables to plugin?

Any clues?

Lee
 
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  • #2
1. Find the marginal distribution of X.

2. Using a 1-dimensional method, draw a simulated value of X based on the marginal distribution-- say it's x0.

3. Fxy(x0, Y) is a 1-dimensional pdf. Use a 1-dimensional method to simulate a value of Y.
 
  • #3
cool, now I can build simulation to check my homework answers.
 

FAQ: Simulating bivariate distribution?

What is a bivariate distribution?

A bivariate distribution is a probability distribution that describes the relationship between two variables. It shows the probability of occurrence of different combinations of values for the two variables.

Why is it important to simulate bivariate distributions?

Simulating bivariate distributions allows us to better understand the relationship between two variables and make predictions about their behavior. It is a useful tool for data analysis, statistical modeling, and decision making.

How do you simulate a bivariate distribution?

To simulate a bivariate distribution, you can use statistical software such as R or Python. First, choose a suitable bivariate distribution model based on the characteristics of your data. Then, use the appropriate function to generate random data points from the chosen distribution.

What are some common bivariate distribution models?

Some common bivariate distribution models include the normal distribution, binomial distribution, beta distribution, and exponential distribution. Each of these models has its own unique characteristics and applications.

How can bivariate distributions be visualized?

Bivariate distributions can be visualized using scatter plots, contour plots, or surface plots. These plots show the relationship between the two variables and can help identify patterns, trends, and outliers in the data.

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