Log-Normal Distribution
Contents
Unraveling Log-Normal Distribution: A Comprehensive Guide
Deciphering Log-Normal Distribution: An Insightful Overview
What is Log-Normal Distribution: A log-normal distribution is a statistical phenomenon that stems from transforming logarithmic values of a related normal distribution. It enables the translation between a log-normal and a normal distribution through logarithmic calculations.
Understanding Normal and Lognormal Distributions:
In the realm of probability distributions, a normal distribution exhibits symmetry, often forming a bell-shaped curve. Within a normal distribution, approximately 68% of outcomes fall within one standard deviation, and 95% fall within two standard deviations.
Conversely, log-normal distributions, derived through logarithmic mathematics, are less commonly understood. Originating from normally distributed random variables, log-normal distributions represent positive variables and are fundamentally interconnected with normal distributions.
Exploring Applications in Finance:
Log-normal distributions offer solutions to limitations posed by normal distributions, particularly regarding the inclusion of only positive variables. In finance, they find prevalent use in analyzing stock prices. While the potential returns of stocks can be depicted using a normal distribution, stock prices are better represented through log-normal distributions. These distributions aid in assessing compound returns over time, exhibiting a positively skewed nature with elongated right tails.
Excel Functionality:
Excel facilitates lognormal distribution calculations through the LOGNORM.DIST function, enabling users to evaluate lognormal distribution probabilities based on mean and standard deviation parameters of the natural logarithm of a variable.
Navigating Lognormal Distribution in Excel
LOGNORM.DIST Function Syntax:
scssLOGNORM.DIST(x, mean, standard_dev, cumulative)
Parameters:
x: The value at which the function is evaluated.Mean: The mean of the natural logarithm of x.Standard Deviation: The standard deviation of the natural logarithm of x (must be positive).