Search results
Results from the WOW.Com Content Network
In statistics, the concept of the shape of a probability distribution arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population.
The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution (a distribution with a single peak), negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness ...
Most simply, they can be estimated in terms of the higher moments, using the method of moments, as in the skewness (3rd moment) or kurtosis (4th moment), if the higher moments are defined and finite. Estimators of shape often involve higher-order statistics (non-linear functions of the data), as in the higher moments, but linear estimators also ...
Both graphs show an identical exponential function of f(x) = 2 x. The graph on the left uses a linear scale, showing clearly an exponential trend. The graph on the right, however uses a logarithmic scale, which generates a straight line. If the graph viewer were not aware of this, the graph would appear to show a linear trend.
Meaning: A k-fold increase in X is associated with an average of units increase in Y. For illustrative purposes, if base-10 logarithm were used instead of natural logarithm in the above transformation and the same symbols ( a and b ) are used to denote the regression coefficients, then a tenfold increase in X would result in an average ...
In statistics, the method of moments is a method of estimation of population parameters.The same principle is used to derive higher moments like skewness and kurtosis. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest.
where S X is the skewness of X and is the standard deviation of X. It follows that the sum of two random variables can be skewed (S X+Y ≠ 0) even if both random variables have zero skew in isolation (S X = 0 and S Y = 0). The standardized rank coskewness RS(X, Y, Z) satisfies the following properties: [4]
Figure 2. Box-plot with whiskers from minimum to maximum Figure 3. Same box-plot with whiskers drawn within the 1.5 IQR value. A boxplot is a standardized way of displaying the dataset based on the five-number summary: the minimum, the maximum, the sample median, and the first and third quartiles.