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Can a log normal distribution be negative?
Key facts about the lognormal distribution All values in a lognormal distribution are positive. Negative values and zeroes are not possible in a lognormal distribution.
Is the variance of a normal distribution always positive?
It measures the degree of variation of individual observations with regard to the mean. It gives a weight to the larger deviations from the mean because it uses the squares of these deviations. A mathematical convenience of this is that the variance is always positive, as squares are always positive (or zero).
Can variance be positive or negative?
Every variance that isn’t zero is a positive number. A variance cannot be negative. That’s because it’s mathematically impossible since you can’t have a negative value resulting from a square.
How is the lognormal distribution different from the normal distribution?
The lognormal distribution differs from the normal distribution in several ways. A major difference is in its shape: the normal distribution is symmetrical, whereas the lognormal distribution is not. Because the values in a lognormal distribution are positive, they create a right-skewed curve. Image by Julie Bang © Investopedia 2019
How to relate lognormal variance and variance of X?
V[log(X)] ≈ E[X] − 2V[X]. This relates to the idea of variance-stabilization; if a dependent variable in a regression has a variance that is proportional to the mean squared, then taking the log of that dependent variable produces something that has constant variance, which is often a desirable or necessary assumption.
Can a normal distribution take a negative value?
A normal distribution may take negative values. If the lognormal distribution is truncated to (1, ∞) so that the normal distribution is truncated to (0, ∞), then the natural log of that “normal” distribution exists. The distribution Norm(50, 2) has almost no probability below 0, so the truncation would have little practical effect in this example.
When to use lognormal distribution to analyze stock prices?
Lognormal is extremely useful when analyzing stock prices. As long as the growth factor used is assumed to be normally distributed (as we assume with the rate of return), then the lognormal distribution makes sense.