Large deviations analysis for the log-normal distribution

Bachelor Thesis (2021)
Author(s)

J.R. Sijsenaar (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Contributor(s)

RICHARD C. KRAAIJ – Mentor (TU Delft - Applied Probability)

P. Chen – Graduation committee member (TU Delft - Statistics)

Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright
© 2021 Jochem Sijsenaar
More Info
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Publication Year
2021
Language
English
Copyright
© 2021 Jochem Sijsenaar
Graduation Date
04-06-2021
Awarding Institution
Delft University of Technology
Programme
Applied Mathematics
Faculty
Electrical Engineering, Mathematics and Computer Science
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Abstract

We inspect the behavior of the probability that a weighted sum of random variables with log-normal tails is greater than its expected value. Under the right conditions for the weights and the variance being set to 1; we were able to bound a suitable transformation of this probability with the upper bound being a fixed factor of the square root of e above the lower bound. Beyond this, we analyse the conditions on the weights and determine a method for letting the weights be random and give an example.
We end off by extending our result to general variance, where we see that the deviation between the lower and upper bound as well as the domain for the result are dependant on the variance.

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