Round 6: Tossup 14

This word names families of distributions for which the mean and variance of the sufficient statistic are derivatives of the log partition function. The natural parameter of a family of distributions denoted by this word is set equal to a linear predictor in the canonical link function of a GLM. This word denotes a special case of the Erlang distribution with shape parameter one, which is the only continuous distribution that is (*) memoryless. The series expansion of a function with this name is used to show that the Poisson PMF sums to one. The inter-arrival times of a Poisson process (10[1])follow a distribution with this name, (10[1]-5[1])whose mean is the reciprocal of its rate parameter lambda. For 10 points, give this name of the function applied to “negative x-squared over two” in the PDF (10[1])of the standard (10[1])normal distribution. ■END■ (0[1])

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