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econmath
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What is the expectation, E(log(x-a)), when x is log normally distributed? Also x-a>0. I am looking for analytical solution or good numerical approximation.
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A log normal distribution is a probability distribution of a random variable whose logarithm follows a normal distribution. It is often used to model data that is skewed to the right, meaning that there are a few large values and many small values.
The expectation of a log normal distribution can be calculated using the formula E[X] = e^(μ+σ^2/2), where μ is the mean and σ is the standard deviation of the corresponding normal distribution.
No, a log normal distribution only includes positive values since the logarithm of a negative number is undefined.
The central limit theorem states that the sum of a large number of independent and identically distributed random variables will follow a normal distribution. Since the logarithm of a log normal distribution follows a normal distribution, this means that the log normal distribution is a result of the central limit theorem.
Some examples include income data, stock prices, population sizes, and the size of particles in a certain substance. Essentially, any data that is skewed to the right and has a few large values and many small values can be modeled using a log normal distribution.