Instruction: Write a function in R that defines a custom probability distribution, including density, distribution, quantile, and random generation functions.
Context: This question tests the candidate's ability to implement custom statistical distributions in R, a skill useful for simulating data and for statistical modeling.
Official answer available
Preview the opening of the answer, then unlock the full walkthrough.
Firstly, defining a custom probability distribution involves creating four key functions: the density function (d), the distribution function (p), the quantile function (q), and the random generation function (r). These components are paramount for comprehensive statistical analysis and simulation.
Let's consider a simple yet illustrative example: a scaled beta distribution. This distribution can serve a wide range of applications due to its flexibility in modeling outcomes that range between two extremes....