The name of this probability density function

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Thread starter Ad VanderVen
Start date Jul 26, 2021
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Density Density function Function Probability Probability density Probability density function

In summary, a probability density function (PDF) is a mathematical function that represents the probability distribution of a continuous random variable. It describes the relative likelihood of a random variable taking on a specific value. Unlike a probability mass function (PMF) which is used for discrete variables, a PDF is used for continuous variables and gives the probability of a range of values occurring. The name "probability density function" refers to the fact that the area under the curve represents the probability of a random variable falling within a certain range. A PDF cannot be negative and is used in statistics to model and analyze continuous data, as well as in hypothesis testing and making predictions.

Jul 26, 2021

Ad VanderVen

TL;DR Summary: Looking for the name of some probability density function.

Does anyone knows the name of the probability density function

f(y) =ae^by-cy²

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Jul 26, 2021

willem2

Isn't that just the normal distibution? Complete the square in the exponent.

Jul 26, 2021

Ad VanderVen

Could be, but this function has support $$y \in (0, \infty)$$.

Jul 26, 2021

RPinPA

Science Advisor

Homework Helper

I think that just makes it a truncated normal.

Jul 27, 2021

Ad VanderVen

I thought so too.

1. What is a probability density function (PDF)?

A probability density function is a mathematical function that describes the probability of a random variable taking on a certain value within a given range. It is used to model continuous random variables, such as height or weight, and is often represented graphically as a curve.

2. What is the purpose of a PDF?

The purpose of a PDF is to show the relative likelihood of different outcomes or values for a continuous random variable. It allows us to calculate the probability of a random variable falling within a certain range of values, and is an important tool in statistical analysis and modeling.

3. How is the name of a PDF determined?

The name of a PDF is determined by the specific characteristics of the function, such as the shape of the curve and the variables involved. For example, a normal distribution PDF is named after the shape of its bell curve, while a beta distribution PDF is named after the beta function used in its formula.

4. What are some common types of PDFs?

Some common types of PDFs include the normal distribution, exponential distribution, beta distribution, and uniform distribution. Each of these PDFs has its own unique shape and characteristics, and is used to model different types of continuous random variables.

5. How are PDFs used in real-world applications?

PDFs are used in a variety of real-world applications, such as in finance, engineering, and social sciences. They can be used to model and predict outcomes in fields such as stock market analysis, risk management, and population studies. PDFs are also used in machine learning and data analysis to understand and make predictions based on large datasets.