A lognormal distribution is a result of the variable " x" being a product of several variables that are identically distributed. It is common in statistics that data be normally distributed for statistical testing. The lognormal distribution can be converted to a normal distribution through mathematical means and vice versa.
The -2.82 is a theoretical Z-score, a.k.a. the value below which we expect 0.237% of our observations to lie on a normal distribution. Now let's calculate the Z-score of our actual data. The 2 outlier dots represent disastrous monthly returns of -20.4% (2008 Financial Crisis) and -22.5% (this past month).
The world of machine learning and data science revolves around the concepts of probability distributions and the core of the probability distribution concept is focused on Normal distributions
Details. The importance of normal distribution comes from the following facts/observations, Many naturally occurring phenomenon seem to follow normal distribution when sample size is large (more on this below). In Bayesian statistics, if you assume a Normal distribution prior on parameters, then posterior distribution is also normal.
Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point. Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution.
Examples: Normal, Student's T, Chi-square, Exponential, etc., Also Read: Basics of Probability for Data Science explained with examples in R. Terminologies. Each PD provides us extra information on the behavior of the data involved. Each PD is given by a probability function that generalizes the probabilities of the outcomes.
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what is normal distribution in data science
