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In probability theory and statistics, the index of dispersion, [1] dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard ...
The variation ratio is a simple measure of statistical dispersion in nominal distributions; it is the simplest measure of qualitative variation. It is defined as the proportion of cases which are not in the mode category: where fm is the frequency (number of cases) of the mode, and N is the total number of cases. While a simple measure, it is ...
I RF = risk-free rate of interest R M = return on the market portfolio σ M = standard deviation of the market portfolio σ P = standard deviation of portfolio (R M – I RF)/σ M is the slope of CML. (R M – I RF) is a measure of the risk premium, or the reward for holding risky portfolio instead of risk-free portfolio. σ M is the risk of ...
Volatility (finance) In finance, volatility (usually denoted by "σ") is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price ...
Deviation (statistics) In mathematics and statistics, deviation serves as a measure to quantify the disparity between an observed value of a variable and another designated value, frequently the mean of that variable. Deviations with respect to the sample mean and the population mean (or "true value") are called errors and residuals, respectively.
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. [1] Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered ...
Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. [1][2] Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the ...
Therefore, a naïve algorithm to calculate the estimated variance is given by the following: Let n ← 0, Sum ← 0, SumSq ← 0. For each datum x: n ← n + 1. Sum ← Sum + x. SumSq ← SumSq + x × x. Var = (SumSq − (Sum × Sum) / n) / (n − 1) This algorithm can easily be adapted to compute the variance of a finite population: simply ...