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Relation between the mean of logarithmized sample values and the mean of non-logarithmized sample values

a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. A random ... more

Probability density function of a log-normal distribution

In probability theory, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, ... more

Standard Error

The standard error (SE) is the standard deviation of the sampling distribution of a statistic. The term may also be used to refer to an estimate of that ... more

Variance

The variance is a parameter that describes, in part, either the actual probability distribution of an observed population of numbers, or the theoretical ... more

Variance of the sample kurtosis of a sample of size n

In statistics and quantitative research methodology, a data sample is a set of data collected and/or selected from a statistical population by a defined ... more

Logarithmic Kurtosis - 4th moment

Is a measure that describes tthe “tailedness” of the probability distribution of a real-valued random variable. Particles logarithmic mean size ... more

Logarithmic Standard Deviation - 2nd moment

Shows how much variation or dispersion from the average exists. Logarithmic mean size (1st moment) needs to be precalculated.

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Generalized volatility for time T

In finance, volatility is a measure for variation of price of a financial instrument over time. An implied volatility is derived from the market price of a ... more

Pearson's moment coefficient of kurtosis (excess kurtosis)

In probability theory and statistics, kurtosis is any measure of the “tailedness” of the probability distribution of a real-valued random ... more

Annualized volatility

In finance, volatility is a measure for variation of price of a financial instrument over time. return is a profit on an investment. It comprises any ... more

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