Is this density function well-known?

In summary, The conversation discusses a random variable Y=e^X, where X follows a standard normal distribution. The probability density function of Y is derived to be f_Y(y)=\frac{e^{-\frac{1}{2} \log^2(y)}}{y\sqrt{2\pi}} and is commonly known as the log-normal distribution. This distribution is explained in detail on Wikipedia.
  • #1
mnb96
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Hello,

in a certain context I had to deal with a random variable [itex]Y=e^X[/itex], where X follows a standard normal distribution, i.e. [itex]X\sim N(0,1)[/itex].
I had to calculate the probability density function of Y, which did not seem to be difficult, and I obtained:
[tex]f_Y(y)=\frac{e^{-\frac{1}{2} \log^2(y)}}{y\sqrt{2\pi}}[/tex]

The question is: does the above density function happen to be so well-known that it already has a name?
 
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  • #2
People call it the log-normal distribution. [It's a silly name: not the log of normal, but rather taking its logarithm gives you something normal. Either way, that's what it's called.]

Wikipedia has a page with the usual basic facts you'd care about: http://en.wikipedia.org/wiki/Log-normal_distribution
 
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1. What is a density function?

A density function is a mathematical function that describes the probability distribution of a continuous random variable. It is used to determine the likelihood of a specific outcome occurring within a given range of values.

2. How is a density function different from a probability function?

A probability function is used to determine the likelihood of a specific outcome occurring for a discrete random variable, while a density function is used for continuous random variables.

3. What makes a density function well-known?

A density function is considered well-known if it is commonly used and recognized in the scientific community, with a significant amount of research and literature published on its properties and applications.

4. Can a density function be used for any type of data?

No, a density function is typically used for continuous data. For discrete data, a probability mass function is used instead.

5. How is a density function calculated?

A density function is calculated by taking the derivative of the cumulative distribution function for a continuous random variable.

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