The probability generating function is defined by Where \(f_X\) is the pdf of distribution X, with an integration analogue forīase of the entropy logarithm, default = 2 (Shannon entropy) The entropy of a (discrete) distribution is defined by If TRUE (default) excess kurtosis returned. The kurtosis of a distribution is defined by the fourth standardised moment, Where \(E_X\) is the expectation of distribution X, \(\mu\) is the mean of theĭistribution and \(\sigma\) is the standard deviation of the distribution. The skewness of a distribution is defined by the third standardised moment, Where \(E_X\) is the expectation of distribution X. The variance of a distribution is defined by the formula Otherwise "all" returns all modes, otherwise specifies The mode of a probability distribution is the point at which the pdf isĪ local maximum, a distribution can be unimodal (one maximum) or multimodal (several With an integration analogue for continuous distributions. The arithmetic mean of a (discrete) probability distribution X is the expectation Upper limit of the Distribution, defined on the Reals.ĭecorators to add to the distribution during construction. Lower limit of the Distribution, defined on the Reals. Arcsine$new(lower = NULL, upper = NULL, decorators = NULL)
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