It seems you've uploaded a mathematical formula related to a distribution function. Here's a summary of what the formulas describe:

1. Probability Density Function (PDF): The first formula provides the probability density function $f(x|\xi, \sigma, u)$ which describes how probabilities are distributed over the values of $x$. There are different expressions for different conditions based on the value of $\xi$. Specifically:

   • When $\xi \neq 0$, the function involves a term like $1 + \xi \left(\frac{x - u}{\sigma}\right)$ raised to a power depending on $\xi$.
   • When $\xi = 0$, the function simplifies to an exponential form.

2. Cumulative Distribution Function (CDF): The second formula defines the cumulative distribution function $F(x|\xi, \sigma, u)$, which is the probability that $X$ will take a value less than or equal to $x$. Similar to the PDF, the CDF also has different forms depending on whether $\xi$ is zero or not.

Do you need a detailed explanation on how to calculate probabilities using these functions, or would you like help with a specific part of this?