On random variate generation for the generalized hyperbolic secant distributions
نویسنده
چکیده
Natural exponential families of distributions have probability mass functions of the form [exp(Ox)]#(dx) where # is a given measure, and 0 > 0 is a parameter. When we compute the mean and the variance, and force the variance to be a quadratic function of the mean as 0 is varied, the number of families becomes severely restricted. Morris (1982) showed that there are in fact only six natural exponential families with this property: the binomial, Poisson, gamma, exponential, negative binomial and N E F G H S families, where GHS is an abbreviation for generalized hyperbolic secant. The N E F G H S distribution with parameters p > 0 and A E IR has density
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