Final answer:
The question involves deriving the inverse transform for the Lomax distribution, which requires finding the CDF and its inverse. Due to incomplete mathematical expressions, detailed derivation steps cannot be provided. The inverse transform method generates random variables from a specified distribution using the CDF.
Step-by-step explanation:
The question asks for the derivation of the inverse transform for a Lomax distribution with parameters α > 0 and λ > 0, which has a density function given as f(x) = α λ (1 + x / λ) −(α + 1) for x > 0. The Lomax distribution is related to the Pareto distribution and is used in various fields such as economics and actuarial science. The inverse transform method is a technique used to generate random variables that follow a given probability distribution by using the cumulative distribution function (CDF) and a uniform random variable.
To derive the inverse transform, we would need to first find the CDF by integrating the density function and then find its inverse. However, in this response, detailed steps for the derivation are not provided as the mathematical expressions are incomplete and require clarification to proceed accurately. Generally, for a continuous random variable X with PDF f(x), the CDF F(x) is obtained by integrating f(x), and the inverse transform F−1(u) is found by solving F(x) = u for x, where u is a uniform random variable on [0, 1].