Metalog4P
A four-term metalog distribution.
The fourth coefficient primarily controls kurtosis. Raising it from zero makes the distribution fatter through its midrange with correspondingly lighter tails, closer to a normal or a symmetric beta than to a logistic; lowering it below zero narrows the midrange and thickens the tails, closer to a Student t with few degrees of freedom.
Two special cases are exact rather than approximate. With the second and third coefficients zero and the fourth positive, the distribution is uniform on the interval of width equal to the fourth coefficient centered on the first. With the third coefficient zero and both the second and fourth positive, it is a mixture of a logistic and a uniform sharing that mean.
Parameters
the location coefficient
the scale coefficient, which must remain strictly positive
the skewness coefficient
the kurtosis coefficient
the lower bound, or negative infinity when unbounded below
the upper bound, or positive infinity when unbounded above
an optional name
Constructors
Functions
Promises to return a random variable that uses the supplied stream number using the supplied stream provider